How to Solve a System of Equations with 3 Variable

How to Solve a System of Equations with 3 Variables

In mathematics, there are many different types of equations that are very commonly used. One of those equations is called a linear equation. These equations most likely look like y=3x+5 or even 2x−y=7. Such equations are called linear equations.

Linear Equation is an equation where the x-variable has a degree of one. When graphed, linear equations produce a straight line in the x-y coordinate plane. A system of linear equations is a collection of two or more linear equations that work together. The most commonly used system of linear equations are systems with two equations. Since linear equations have two variables, x and y, then the simplest of a system of linear equations will have two equations. This way, it is possible to solve for a value of x as well as y.

However, a system of linear equations is not limited to just two equations. As the definition stated, a system can have two or more equations. This means that it is also possible to have a system that has three equations. If there are three equations in the system, that means there are three variables in each linear equation, for example, x, y, and z. When it comes to graphs, a system of equations with only two equations is graphed in the 2D x-y coordinate plane. But, a system of equations with three variables is graphed in the 3D x-y-z plane. Take a look at the image below to see an example of a system of equations that has three equations.

 

Example of a System of Equations in Three Variables
system of equations

 

There are three types of solutions that can be obtained when trying to determine the number of solutions for linear systems: one solution, no solution, or infinite solutions. This lesson will focus on how to solve a system of equations with three variables.

How to Determine the Number of Solutions for Linear Systems

When systems with three variables have one solution, it means that there is exactly one location on the 3D plane where all three lines will intersect. In other words, there is exactly one value of x, y, and z that satisfies all three equations within the system. Take a look at the image below to see how to solve a linear system with one solution. Notice how there is exactly one solution for each of the three variables, giving a final solution of (1/2, -2, 2).

 

3-Variable System with One Solution
3 variable system

 

How to Solve a System of Equations with Infinite Solutions

When linear systems in three variables have infinite solutions, this means that linear equations are coinciding. In other words, they produce the exact same equation and lie on top of one another. This means that every single x, y, and z value will satisfy all three equations. Take a look at the image below to see how to solve a linear system with infinite solutions. Notice how the equation in step 1 produces the exact same equation in step 2.

 

3-Variable System with Infinite Solutions
system or equations

 

How to Solve a System of Equations with No Solutions

When a system of linear equations three variables has no solution, this means that there are three equations parallel to each other and therefore will never intersect. If the two equations never intersect, then there will never be an x, y, or z value that satisfies all three equations. Take a look at the image below to see how to solve a linear system with no solutions. Notice how step one gets a value for x that is not equal to the value of x in the next step. Since there is more than one value that can be obtained by x, then there is no solution.

 

3-Variable System with No Solutions
Systems of Equations

 

Practice Solving Linear Systems with 3 Variables

Example 1: Solve the following system of equations:

 

Example 1
Systems

 

To begin this problem, determine two equations that can be used to easily eliminate one of the three variables. Take a look at the three given equations. The first equation and the third equation have the variable z written as an exact opposite of each other. In the first equation, there is a positive z, and in the second equation, there is a negative z, allowing for these two equations to immediately cancel each other out. Therefore, for the very first step, add together 2x+4y+z=1 and x+y−z=−1 to get the new equation 3x+5y=0.

For the next step, since z in the first equation needs to be eliminated, use two more equations to replace z. The best way to complete this is by using the first equation and the second equation. However, before adding these two equations together, frame one of the equations such that z can be properly replaced. Looking at the two equations, if the first equation is multiplied by 3, then it will change to 6x+12y+3z=3, which can then be successfully eliminated by the negative 3z in the second equation. Therefore after adding together the manipulated equation, 6x+12y+3z=3 and the third equation x−2y−3z=2, one can get another new equation, 7x+10y=5.

Next, since the two new equations created are written with x and y variables, use those two equations to eliminate one of the variables. Notice that the first equation has a 5y, and the second equation has a 10y. This means that the first equation can be multiplied by -2, thus successfully eliminating the y-variable. By multiplying the first equation with -2, it becomes −6x−10y=0. Now, add this to the second equation, 7x+10y=5. This will eliminate y and leave the value of x with x=5.

Now that value of x is successfully solved, use this value of x to solve for y. By using the first equation that is created, 3x+5y=0, plug in the value of x to successfully solve for y. By placing value of x as 5, resultant becomes 3(5)+5y=0, which is 15+5y=0. Then subtract 15 on both sides to get 5y=−15 and then divide it by five into both sides to get y=−3.

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Linear Equation Definition

Linear Equation Definition

An equation relies on the word “equal” so an equation is simply a math statement that includes two, or more, things being set equal to each other. For example, 3+2 is not an equation, but 3+2=5 is an equation simply based on the equal sign. This holds true even if it uses letters, symbols, or the Greek alphabet instead of numbers.

Something linear is related to a line. So a linear equation is an equation that when graphed makes a line. A linear equation can have one, two, three, or more variables.

Graph of two linear equations
two linear equations, linear equation graph

 

Forms of Linear Equations

The general form of a linear equation is y = mx + c. This equation gives us some key information about the linear equation meaning. The slope is represented by m and the x-intercept is represented by c. So in the equation y = 3x + 2 it is already known that there will be one point at (0, 2) and the slope will be 3. Remember slope is “rise over run” so a slope of 3 would mean rising or going up 3 and running or going to the right 1. From this, another point on this line can be found by adding 3 to the y value (the rise) and 1 to the x value (the run). Another point on this line would be (1, 5). If the dots are connected and the line extended in both directions, a graph of the linear equations has been achieved.

The general form of the linear equation can be re arranged so it might look different. It might appear as:

  • y – c = mx
  • y – mx = c
  • y – mx – c = 0
  • c + mx = y

Each of these can be rearranged to get it back to the more desirable y = mx + c format. Other linear equations might appear to be missing a part: y = c or y = mx, for example. In these cases, the missing part must be equal to 0. If the linear function is in y = c format or even x = any number this is considered a constant function or identity function. If the y = c then the line will be horizontal or flat. For every value of x the y value will be the same. If it is x = any number then the line will be vertical. For any value of y the x value will remain the same.

Linear Equation Constant Function
Linear Equation Constant Function

 

Linear Equation Examples

The easiest linear equations are the constant function or the identity function where y = c or x = any number. In real life, this might be an age in years for any month that doesn’t include that person’s birthday. It will remain constant throughout the month. Here are some linear equation examples:

  • y = 15
  • x = 32

Two variable linear equations fit the general form of y = mx + c. In real life this might help someone determine the cost of a ride share. For example, if it costs $1 for the driver to pick up plus $0.20 per mile, a linear equation of y = .2x + 1 can be created to determine the cost. Here are some other linear equation examples with two variables:

  • y = 1 + .2x
  • .2x = y – 1
  • .2x – y + 1 = 0

Just because an equation has two variables doesn’t always mean it will be linear. There could also be a parabola (y = x squared – 3) or a circle ( y = 2 = the square root of (25 -x)). Remember if the graph has any type of curve and not just a line, then it will not be considered linear. We call these types of equations non-linear.

Three variable linear equations in real life might include trying to meal plan when limited on calories, fat, and sugar. For example, if only three meals are eaten with no snacks, and the limit of calories is 2,000, the limit of fat is 20 grams, and the limit of sugar is 20 grams, a system of linear equations can be created. Assume b stands for breakfast, l for lunch, and d for dinner.

  • b + l + d = 2000 calories
  • b + l + d = 20 grams of fat
  • b + l + d = 20 grams of sugar

For linear equation examples with four or more variables, it is apparent that someone could simply add more meals, snacks, or drinks to the above equations. They could also subtract calories burned off when working out.

  • b + l + d + s = 2000 calories
  • b + l + d + s – exercise = 2000 calories

System of Linear Equations

system of linear equations is a group of linear equations that work together. These can be graphed to solve for different information. Let’s look at some system of linear equation examples.

I want to use rideshare and I have two different apps available. One has a higher initial cost to pick me up than the other, but it also has a lower cost per mile. I need to know which one will cost me the least amount of money. Option A: Pick up costs $1 and $0.20 per mile. Option B: Pick up costs $2 and $0.15 per mile. I can use this information to create two linear equations.

  • y = .2x + 1
  • y = .15x + 2

I could plug in the number of miles for each to determine which is cheaper this time. Or I could solve the system of equations so I will always know at what point I should switch from one company to the other.

I want to open a lemonade stand and I need to buy lemons, sugar, and cups. I have $20 to spend. What is the maximum amount I can buy?

  • l + s + c = $20

For every 6 servings, I need 6 lemons, 1 cup of sugar, and 6 cups. I need to balance my shopping to maximize the amount of lemonade I can make. I don’t want to end up with extra lemons and sugar and no cups to serve it in. These are just some examples of when it is helpful to understand systems of linear equations.

Solution of Linear Systems

If we are told all equations are said to be true, then there are three possible outcomes when solving a system of linear equations. It might be found that there are no solutions, exactly one solution, or there is an infinite number of solutions. This is true, no matter which method is used to solve the system of equations:

  • Graphing
  • Substitution
  • Elimination
  • Row Reduction
  • Determinant

If all of the equations given can be rearranged into the exact same equation or graphed and displayed as the same line, then one can say there are infinitely many solutions. It doesn’t matter what number is put into it, a solution to the linear system will always be able to be found. This is considered a dependent system of equations.

Infinite Solutions to a Linear Equation
Linear Equation All Solutions Infinite

System of Linear Equations – Geometrical Meaning

System of Linear Equations – Geometrical Meaning

Review Terms

linear equation is an equation where the unknowns or variables are powers with exponent one.

For example, 3x – 4y + 5z = 3 is a linear equation because the variables xyz are linear, but xy + 3z = 7 is not linear because of the term xy, which is a product of two variables.

Geometric Meaning of a Linear Equation

A linear equation ax + by = c, represented in the rectangular coordinates is a line with slope -a/c, while a linear equation of three variables, ax + by + cz = d, is a plane in space, whose normal vector is <a, b, c>.

When we solve a system of linear equations, we look for a solution that verifies all equations in the system, or the solution is at the intersection of all equations.

Geometric Meaning of a System of Linear Equations

Therefore, a system of two linear equations with two unknowns represents the intersection of the two lines in a plane, and a system of three linear equations with three unknowns represents the intersection of three planes in space.

Because the intersection of three planes in space could be a point (when the three planes intersect in a single point), one line (when all three planes contain the line), one plane (when all three planes are identical), or empty set (when there is no common intersection to all three planes).

Similarly, we have three types of solutions to a system of three equations: unique, infinitely many, or no solution.

Application

For each of the systems of equations, determine and give the geometric meaning (if any) of the solution.

1.

 

2.

 

3.

 

Solutions

1. Using back substitution, we obtain the unique solution x = 1y = 3z = -1, which is a point.

2. No solution. The last two equations are inconsistent.

3. Infinitely many solutions, the first and third equations are equivalent.

 

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Systems of Linear Equations with Examples

Science Courses / HESI Admission Assessment (A2) Exam / HESI Admission Assessment Exam: Linear Equations, Inequalities & Functions
Systems of Linear Equations with Examples

Linear Equation Definition
An equation relies on the word “equal” so an equation is simply a math statement that includes two, or more, things being set equal to each other. For example, 3+2 is not an equation, but 3+2=5 is an equation simply based on the equal sign. This holds true even if it uses letters, symbols, or the Greek alphabet instead of numbers.

Something linear is related to a line. So a linear equation is an equation that when graphed makes a line. A linear equation can have one, two, three, or more variables.

Graph of two linear equations

two linear equations, linear equation graph
Forms of Linear Equations
The general form of a linear equation is y = mx + c. This equation gives us some key information about the linear equation meaning. The slope is represented by m and the x-intercept is represented by c. So in the equation y = 3x + 2 it is already known that there will be one point at (0, 2) and the slope will be 3. Remember slope is “rise over run” so a slope of 3 would mean rising or going up 3 and running or going to the right 1. From this, another point on this line can be found by adding 3 to the y value (the rise) and 1 to the x value (the run). Another point on this line would be (1, 5). If the dots are connected and the line extended in both directions, a graph of the linear equations has been achieved.

The general form of the linear equation can be re arranged so it might look different. It might appear as:

y – c = mx
y – mx = c
y – mx – c = 0
c + mx = y
Each of these can be rearranged to get it back to the more desirable y = mx + c format. Other linear equations might appear to be missing a part: y = c or y = mx, for example. In these cases, the missing part must be equal to 0. If the linear function is in y = c format or even x = any number this is considered a constant function or identity function. If the y = c then the line will be horizontal or flat. For every value of x the y value will be the same. If it is x = any number then the line will be vertical. For any value of y the x value will remain the same.

Linear Equation Constant Function

Linear Equation Constant Function
Linear Equation Examples
The easiest linear equations are the constant function or the identity function where y = c or x = any number. In real life, this might be an age in years for any month that doesn’t include that person’s birthday. It will remain constant throughout the month. Here are some linear equation examples:

y = 15
x = 32
Two variable linear equations fit the general form of y = mx + c. In real life this might help someone determine the cost of a ride share. For example, if it costs $1 for the driver to pick up plus $0.20 per mile, a linear equation of y = .2x + 1 can be created to determine the cost. Here are some other linear equation examples with two variables:

y = 1 + .2x
.2x = y – 1
.2x – y + 1 = 0
Just because an equation has two variables doesn’t always mean it will be linear. There could also be a parabola (y = x squared – 3) or a circle ( y = 2 = the square root of (25 -x)). Remember if the graph has any type of curve and not just a line, then it will not be considered linear. We call these types of equations non-linear.

Three variable linear equations in real life might include trying to meal plan when limited on calories, fat, and sugar. For example, if only three meals are eaten with no snacks, and the limit of calories is 2,000, the limit of fat is 20 grams, and the limit of sugar is 20 grams, a system of linear equations can be created. Assume b stands for breakfast, l for lunch, and d for dinner.

b + l + d = 2000 calories
b + l + d = 20 grams of fat
b + l + d = 20 grams of sugar
For linear equation examples with four or more variables, it is apparent that someone could simply add more meals, snacks, or drinks to the above equations. They could also subtract calories burned off when working out.

b + l + d + s = 2000 calories
b + l + d + s – exercise = 2000 calories

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System of Linear Equations
A system of linear equations is a group of linear equations that work together. These can be graphed to solve for different information. Let’s look at some system of linear equation examples.

I want to use rideshare and I have two different apps available. One has a higher initial cost to pick me up than the other, but it also has a lower cost per mile. I need to know which one will cost me the least amount of money. Option A: Pick up costs $1 and $0.20 per mile. Option B: Pick up costs $2 and $0.15 per mile. I can use this information to create two linear equations.

y = .2x + 1
y = .15x + 2
I could plug in the number of miles for each to determine which is cheaper this time. Or I could solve the system of equations so I will always know at what point I should switch from one company to the other.

I want to open a lemonade stand and I need to buy lemons, sugar, and cups. I have $20 to spend. What is the maximum amount I can buy?

l + s + c = $20
For every 6 servings, I need 6 lemons, 1 cup of sugar, and 6 cups. I need to balance my shopping to maximize the amount of lemonade I can make. I don’t want to end up with extra lemons and sugar and no cups to serve it in. These are just some examples of when it is helpful to understand systems of linear equations.

Solution of Linear Systems
If we are told all equations are said to be true, then there are three possible outcomes when solving a system of linear equations. It might be found that there are no solutions, exactly one solution, or there is an infinite number of solutions. This is true, no matter which method is used to solve the system of equations:

Graphing
Substitution
Elimination
Row Reduction
Determinant
If all of the equations given can be rearranged into the exact same equation or graphed and displayed as the same line, then one can say there are infinitely many solutions. It doesn’t matter what number is put into it, a solution to the linear system will always be able to be found. This is considered a dependent system of equations.

Infinite Solutions to a Linear Equation

The First Amendment: Commercial Speech, Scrutiny & Restrictions – Quiz & Worksheet

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The First Amendment: Commercial Speech, Scrutiny & Restrictions – Quiz & Worksheet
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30 Best Business Ideas for the USA – 2022 and Beyond

30 Best Business Ideas for the USA – 2022 and Beyond
The business landscape in the United States is always changing. New technologies, trends, and policies all contribute to the changing business landscape. Since so many changes have been made in the recent years, I thought it was time for some new business ideas for the USA to be presented. Below are 30 business ideas based off of recent industry research and designed for 2022 and beyond.

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1. E-Commerce distribution center for small business
E-commerce in the USA grew to over $450 billion in 2017, a 16% increase from 2016. However, with these enticing statistic, the huge presence of Amazon.com creates tough competition for small businesses. This business idea would help fix that by creating a service where small businesses can have their products shipped to, for storage and distribution. Ultimately helping manage their online sales. This also takes out the complications of managing that operation for the small business owners. With the market set to grow further, this idea is one to watch.

E-commerce retail sales trends related to business ideas for USA
2. Retail & Distribution Consulting
Many retail commercial spaces are becoming ghost towns as people continue to shift to purchasing stuff online. A unique trend that has already been established in China is using the retail outlet spaces for both customers and distribution. They shrink the front space to make room for a space in the back for distribution. To execute on this idea, one could approach mid-sized companies with retail storefronts that do not get much foot traffic, and consult them on how to better utilize their space. This will be a growing need for businesses as the e-commerce trend continues.

3. International Trade Consulting Company
Since Trump’s presidency, there have been a lot of changes and more potential changes coming with international trade. This company would help other companies keep up and manage these changes in regulations, tariffs, and other uncertainties. As other countries change their policies, there will be more demand for this idea.

4. Personal CyberSecurity Software Company
Cybersecurity threats continue to increase year over year, and the severity of the threats keeps increasing. For instance, look at the recent Equifax hack, millions were affected. Almost everyone has a smartphone with several social media accounts, online banking, personal photos, and other important information. Many people don’t have this protected. This idea would cater to the executives and rich who really need their personal information secure at all time. As online services grow, so does the potential for this company, as more cyber attacks happen.

5. Small Business CyberSecurity Software Company
Again, with the increases in cybersecurity threats, many small businesses are vulnerable to attacks and threats too. Many of them also cannot afford big name software systems or an IT department to get things under control. By developing a software that would protect all the basic areas of a small business, you could serve 98% of the business community in the United States.

CEO Threat Cyber Threats and how business idea for USA can save it

6. Security Company (Drone powered)
With the use of drones, one can provide surveillance to large areas using thermal and HD cameras. It can also prevent the threat to human security employees from any harm from robbers or other threats. This is also an idea that can be started with little money (surprisingly). All you would need to do is buy a drone that is quiet, has thermal, noise, and HD capabilities. In total, it costing about $1,500 if you shop smart. Then you could go and get security contracts for large pieces of land.

7. Digital Assistant Integrations Company
Many large corporations provide assistants to the executives. However, the one downfall is that the executives can work a lot longer than their assistants do, leaving them without help sometimes. With the growth and rise of artificial intelligence (AI), personal digital assistants could be the perfect replacement. If you have interest or knowledge in developing personal assistants for executives to process calls, book meeting times, flights, arrange printings etc, then this idea would be perfect for you.

Ai growth in GDP

8. School of the Future
The rise of AI over the next decade is going to disrupt how people work in general. This will change the needs of the schooling institutions that prepare our youth for the future. The school of the future idea would be a private school, teaching people the skills they need to compete and operate with AI. For instance, soft skills are going to be in higher demand than ever before. If you have a passion for education, you should definitely think about this type of idea.

Displaced workers by AI and idea to solve problem
9. Corporate Immigration Consultant
Again, since Trump has taken over the White House, there has been a lot of changes to the immigration laws. To the contrary, there are a lot of businesses in America that rely on immigrants for top talent. For instance, there is a shortage of quality computer programmers in the USA so many of them need to be hired abroad. The changes in policy also complicate things where other businesses need help navigating this area. This idea would help fill that complication.

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10. AI Implementation company
With over 35% of executives looking into the implementation and investment into AI, there is definitely need for an AI implementation business. For this idea, you would be using other AI software that other companies developed, in conjunction with reliable data gathered for the inputs to create useful systems that other companies could use. There will be a huge demand for this among fortune 500 companies for this service.

AI & Executives Investment for ideas in USA
11. Affordable Elderly Care Facilities
The growing elderly population is apparent in the USA, and there is a huge need for affordable elderly care facilities. These facilities will also need to provide quality treatment, as there have been past problems with bad quality managed facilities. This business idea would be in high demand since there are many elders who rely solely on government subsidies or little pensions provided by companies that went bankrupt.

12. Opioid Addiction Facility
A cost-effective opioid addiction treatment facility would be a high-demand business due to the epidemic that the United States is facing. Both legal and illegal opioids are causing a lot of addiction problems. To fight this, one could open up a facility in the most vulnerable states. The best way to do this without sinking a lot of your own money would be to look for state grants that could provide funding. This is the perfect business idea for someone wanting to do good in the world, and fight the opioid epidemic.

opiod crisis graph
13. Chatbot Developer
Chatbots are growing in demand year over year. Small and large businesses have huge uses for chatbots. They provide customer service, help with complaints or reviews, and even serve the site visitor content when appropriate. As a point of differentiation, you can niche down and target a specific group so you can fulfill their needs completely. For example, a chatbot for independent financial advisors could help potential clients navigate the site and get to know them further. This idea will take strong programming skills to develop and deploy.

14. MRI Scanning Service
Getting an MRI scan can take months in some cases. This is because there is such a backlog of people that need them. The MRI Scanning service business idea would be a company that would provide mobile MRI scans. By setting up a stabilized truck and trailer, you could drive to high-demand areas, and provide MRI scans to multiple people in the area that need it. This would avoid the cost and hassle of having a brick and mortar facility where people need to come to.

15. Virtual Doctor Company
The baby boomer generation is a large part of the United States population, and they account for a significant amount of the total healthcare spend. This means they are an important demographic to watch. The virtual doctor company would help this demographic by allowing them to see doctors are reduced rates and without the hassle of having to leave home. Since there is an increasing amount of baby boomers with mobility issues, staying home works well for them too. If you have computer programming skills, this could be a great business idea.

Aging population visit doctor online

16. Custom Content Creation AI Service
Another artificial intelligence business idea. This one is designed as a tool for digital marketers to create custom infographics or blog content. To create a solid business from this, you would need to seek investment so you can build a team to help with this idea. Imagine a software tool that you could plug in your competitors, your own site, and the kind of content you wanted to create, and this tool would develop and post it for you. Although all content needs a slight human touch, this would be a game changer when it comes to content creation for marketers.

17. API Management Firm
APIs are ways that online companies can let others access important data from their platforms and integrate them into their companies. For example, Google has different APIs that you can access to pull data from, and put into other programs for business use. The use of APIs are on the rise, and they will only become more popular as the use of data increases. The API management business idea would help other mid-sized companies setup and manage their API so customers or partners can access important information from that company. If you have strong knowledge of IT, then this idea is a great fit.

18. “Lean Data” Collection Software and Storage Company
The world of data is starting to overwhelm the very companies that create it. The lean data software collection company would provide software systems that can mine the data created by these companies in an efficient and insightful matter. If you are a data scientist, or love data, then this business idea is for you. Fortune 500 companies would pay you a lot of money for software that could collect only the important information. It would save on server costs, data management, and other costs for the companies that implement it.

Global amount of data produced each day 2017

19. The No Cashier Store Conversion Company
Amazon was the first to open the gates to the stores with no checkouts and cashiers. However, they weren’t the first in the world to do this. China has been doing this for years, so don’t get scared of someone like Amazon coming into this space. Imagine if you could walk into any small business, walk out with the clothes you want, and not have to worry about paying as it could be charged to your bank automatically.

20. Smart Shopping Cart Developer
This is another business idea designed around eliminating the cashiers at the till. As the self-checkouts become more popular, and the demand for quick service grows, so will these business ideas for the USA. Also, many people hate waiting at the grocery store and the checkout lines are the bottleneck in the operation. By removing the checkouts with smart carts that know everything in them, one could simply just pay for their groceries through an app. A strong technology and coding background would compliment this idea nicely.

21. Hyper-Local Small Business Marketing Company
Hyper-local marketing is a rising trend that is only going to become more apparent. As more businesses pop-up as the years passes by, more and more markets become saturated. At this point, many businesses face the challenge of competing for market share. Hyper-local marketing can fill that need by creating very specific messaging and communications to local areas such as towns and cities, one by one. I can already sense this will be one of many successful business ideas.

22. Augmented Reality Analytics Software Company
This idea is designed to complement the growing Augmented Reality (AR) marketplace. It has been clear over the past few years that AR is going to overtake virtual reality (VR). This growing demand makes getting into the analytics business attractive. All new businesses need analytics to see what their users are doing, especially an AR company. The software in this idea would be able to track where the users look, how they interact, and other useful insights that developers need for future improvements.

Benefits of AR in workplace by country

23. All-in-One Small Business Platform
This all-in-one small business platform idea would help the business owners that get overwhelmed with everything, which can be fair. It can become tricky managing employees and different systems, etc. This software platform would solve those needs by providing a hub where they could see their business holistically. For example, they would be able to see the finances, operations, sales, marketing, HR, and other departments all through one program, and manage the needs of each one through the software. Although it is a bit out there and extremely complex, this business idea would solve problems and break down the barriers to entering entrepreneurship.

24. Remote Worker Integration Company
There is rising demand from the workforce to be able to work from home. Not everyone wants to get on a bus or in a car to get to the workplace, and some people are happy to work from home. In fact, people are demanding it. To execute on this idea, you would need to help small to medium-sized companies integrate security and other software to manage their remote employees. Things that would need to be setup would include a VPN, security software, other working software applications that the employee needs on a remote laptop, etc. If you have strong IT skills, this a business opportunity you won’t want to miss.

Percentage of corporate workers who want to work from home
25. Wireless Car Fleet Management Company
Driverless cars are coming and they are going to change the way people live. The question is, are you going to be at the front of these changes or will you be watching them as it happens? With this company, you could be leading the way. Many companies in the USA rely on fleets of vehicles to get the work done for their customers. For example, a cable installation company may have a fleet of vans for their workers. With the autonomous cars, you could manage the fleets of cars including wireless vehicle inspections, regular maintenance, and roadside assistance due to the capabilities to monitor all this wirelessly. Secondly, the companies would save on insurance costs since the cars are controlled by robots and would be safer than humans driving.

Finding the fit ebook banner 2

26. Blockchain Supply Chain Development
Many companies tell their customers that they use certain ingredients or source their material from sustainable methods, however, as a consumer, there is no true way of proving this unless you look inside their books. For companies to strengthen their brands, they could use blockchain operated supply chains, and you could build them for these brands. For example, a butcher may want to prove to you on the receipt, that the meat he got was raised and sourced from a local town or nearby. Then you know exactly where your food is coming from and you can trust them completely as it is transparent. This is just one example of many. Have an interest in blockchain? This idea will be a game changer.

27. Real Estate Title Management Blockchain Software
Another blockchain business idea. This one has to do with the management of the real estate titles for properties. When you buy or sell a home, you or your realtor will give notice to the proper authorities of the land title change, so it is recorded. However, the current process for this is costly and inefficient with long wait times (several days). Luckily, with blockchain technology, one can solve this problem. As soon as a house is sold, the buyers and sellers would simply need to verify who they are with their unique key, and how the property transferred, and then it would be done. If you don’t start this idea, I guarantee it will be started soon.

28. Marijuana Testing and Compliance Company
The legalization of marijuana is a touchy subject for many, however, there is a lot of profit to be made with the deregulation. Several states have already taken action and have legalized it for recreational and medical uses. Canada is on the road to legalization, so it won’t be very many years from now (in my prediction) that the USA will follow. That is when things could explode. In the meantime, the testing and compliance side of the business is ripe for entry because the industry is so new. The idea would involve monitoring the quality of product sold to people to monitor for health issues. If you like cannabis, this is a business idea you should consider.

Marijuanna Laws by State Map for USA business ideas
29. Aftermarket Electric Car Part Manufacturer
There is a growing market for electric cars. Tesla created a great initial wave of demand with their electric cars, and now other car manufacturers are quickly following. Similar to gas and diesel car and trucks, there are aftermarket parts that you can get to further customize your vehicle. With the rise of electric cars, this leaves a market partially open for you to enter and make money. To execute you would need a strong knowledge of cars, and what types of modifications or aftermarket parts electric car drivers want.

30. Online DNA Pattern Reading Company
Having your DNA pattern read to determine how your body will perform in the future is a weird thing to think about, but a not so distant reality. These days, it costs about $600 to map your DNA. This is a fraction of the cost years ago. This company would cater to those who want to find out if they will get genetic diseases as they grow old. It can also help prevent certain diseases by taking action before symptoms arise. If you have a strong interest in science and medicine, this idea is

What is Validity and Reliability in Research?

Types of Research Design
Over the years, the field of psychology has attempted to answer complicated questions about human nature, such as:

What treatments are effective for mental illness?
What is the most effective way to teach children?
What makes people happy?
Answers to these questions can only come from high quality research. This lesson will cover many different types of research design and give an example of each.

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Cross-Sectional vs. Longitudinal Design
The first decision a researcher must make is whether to test a group of people at a single moment in time or whether to test a group of people several times, across many days, weeks or even years. Imagine you need to make this decision. What are the pros and cons of each choice?

If you decide that you are going to study a group of people just one time, in a single session, that research design is called cross-sectional research. An obvious pro, or advantage, to cross-sectional research is that it is relatively easy and inexpensive. It’s also easier to do your study using a large group of people because you only need them for a single session. It’s easier to get people to agree to be in a study if it only takes a single hour or single day. However, a con, or disadvantage, to cross-sectional research is that you cannot study whether people change over time. That’s where the second type of research comes into play.

If you decide that you want to study a certain group of people over multiple sessions, or over an extended period of time, that research design is called longitudinal research. You can remember the name ‘longitudinal’ because it starts with the word ‘long,’ meaning a long period of time. The advantages and disadvantages of longitudinal research are the exact opposite of cross-sectional research. With longitudinal research, you can follow people over time, which means that you can see how their thoughts or behaviors change across different locations, when they are around different people or simply as they age.

For example, imagine you are studying happiness. You could study whether someone who is happy today is still happy next week, next month and next year. In this way, you might gain insight into the stability of emotions by using longitudinal research. However, the disadvantage of longitudinal research is that it is more expensive and time consuming, and often it’s difficult to get volunteers for the study due to their increased time commitment.

Types of Studies
The difference between cross-sectional and longitudinal research applies to every particular type of study. Next, we need to cover different types of studies. Again, each choice has advantages and disadvantages.

Imagine that you want to study happiness in children. This example will be used for the rest of the lesson to illustrate the differences between each type of research design.

Case Studies
The first option you have is called a case study. A case study is defined as the use of a single person in a research study. For our example of studying happiness in children, imagine that a particular child has been identified by his teachers as always being extremely happy. A researcher might study this child in-depth to attempt to understand why he is so happy.

The advantage of a case study is that it allows a researcher to gain a lot of in-depth, detailed information due to the close examination of this single case. However, a disadvantage is that what you learn about this particular person might not be true of anyone else. So, it may be difficult to make general conclusions about what makes other people happy because you only really know about this single person.

Field Studies
The next option researchers have is called a field study, or sometimes this is called a naturalistic study. Here, instead of asking participants to come to a strange lab to be studied, the experimenters observe the participants in their natural environments.

For example, if you wanted to study happiness in children, you might observe children at school or on a playground. Don’t get confused and think that just because it’s called a ‘field’ study, you actually have to go out into a field! The term simply means that you are not in a lab. Instead, you are in a natural environment.

The advantage of a field study is that the behaviors you observe will certainly be more natural because, ideally, you are simply watching what would have happened anyway, even if you weren’t there. The disadvantage of a field study is that you have no control over the environment, so you can’t really test the impact of changes to that environment, and you can’t really ask the participants any questions because that would be interrupting their natural behaviors.

Survey Studies
Perhaps the most common type of research in psychology is a survey study. This is exactly what it sounds like. Researchers give a group of people a survey with lots of questions, and the participants simply answer the questions. For example, a researcher could ask every child in a certain school to fill out a questionnaire about what makes them happy or unhappy.

The clear advantage to this type of study is that it is easy, simple and inexpensive, and a researcher can get hundreds of people to complete the survey in a relatively short period of time. However, there are some disadvantages to survey studies. One disadvantage is that it’s difficult to truly test the impact of certain variables when all people are doing is filling out a survey. Another disadvantage is that some people might not be honest in their survey responses.

 

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What is Sociological Research? – Positivist, Interpretive and Critical Approaches

Sociological Research
No one lives in a vacuum. People interact with society every day. Even if you stay in your room all day and don’t go outside, you are still expected to obey the laws and rules of society. You might turn on your computer, watch television or read a book or magazine, all of which are influenced by society. In short, everyone is influenced by society.

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Sociology is the study of human society and its patterns. Sociologists do research on the problems and development of societies and the ways that humans interact. For example, a sociologist might look at how a specific society deals with public health issues like obesity. What does the society do? How do people in the society view the issue? What things work to combat the problem?

Whether they are looking at class, gender, race, social movement or one of many other topics, sociologists do research by analyzing statistics, languages and the social movements of societies. There are three main lenses through which sociologists look at society: positivist, interpretivist and critical theories. Let’s look closer at each one.

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Positivist Sociology
Imagine that you are a sociologist. You’ve noticed a trend in your culture that voting is low among poor and young people. Older, richer people are still voting regularly, but people who are not part of the upper class and/or older generation are voting less and less as the years pass. You want to know why this is happening.

How do you go about studying this phenomenon? Positivist sociology studies the rules that govern behavior in society through a scientific lens. If you are a positivist sociologist, you are interested in the science of society. You want to apply the scientific method and scientific tools to your studies to find the natural laws of human behavior within society.

You know how people are bound by the laws of gravity? Science has tested and shown that gravity is a natural force that works on human bodies. Positivism looks at sociology the same way that scientists look at gravity; it says that there are certain natural forces that work on societies, and they should be studied in a scientific manner.

So, let’s go back to our scenario. You’re a sociologist, and you want to study why younger, poor people are not voting. As a positivist sociologist, you might look for an external force that causes this to happen. Is it because younger, poorer people are less educated and therefore less likely to follow elections?

Let’s say that education is your hypothesized cause of lower voting among certain parts of society. You want to test this hypothesis using tools like surveys and statistical analysis. This is the essence of positivist sociology; you develop a hypothesis about the forces at work in society and test it using scientific tools.

The essence of positivist sociology is testing hypotheses using scientific tools.
Positivist Sociology

Key Sociology Theorists Chapter Exam

1.
This sociologist believed that knowledge was the crucial element to social change, and that it is the job of social scientists to connect individual problems with greater social issues in order to create changes that would solve these problems.

C. Wright Mills
Herbert Spencer
Charles Cooley
Karl Marx
2.
A _____ is an organization with a well-defined formal hierarchy and chain of command, with competence rather than personality as the basis for job appointment.

corporation
bureaucracy
gesellschaft
gemeinschaft
3.
This sociologist developed the functional perspective theory of society, which views society as an organism with various parts that each have a function to perform.

Robert Merton
Erving Goffman
W.E.B. Du Bois
Karl Marx
4.
W.E.B. Du Bois developed the idea of _____, which explained what it was like for black people living in a white world.

double consciousness
double impression
racial consciousness
dramaturgy
5.
All of the following statements concerning Karl Marx and his works and ideas are true, EXCEPT:

He disagreed with capitalism because he believed it would lead to a wider gap between the rich and poor.
He believed that social class determined a person’s social life, and that the people who owned modes of production would control the lower working class.
All of the answer choices are true.
The revolutions he hoped for in large industrial countries such as Germany did not occur due to factors like the development of labor unions.

Sociology 101: Intro to Sociology

Introduction to Sociology: The Basics Learn the definition of sociology and why it is important. Research some basic theories and perspectives related to sociology.
Key Sociology Theorists Study the works of sociology theorists, including Marx, Weber, Durkheim, and Du Bois.
Sociology Research Methods Find out what types of research methods are used in sociology. See how research is interpreted and used.
Foundations of Society Discover the elements and perceptions of culture. Study social interaction theory alongside the various agents of socialization.
Theories of Individual Social Development Look at theories explaining individuals’ social development. Survey the perspectives of Freud, Piaget, Kohlberg, Gilligan, Mead, and Erikson.
Social Groups & Organizations Learn how social groups form and explore the characteristics of these groups. Study such concepts as groupthink, social loafing and social conformity.
Diversity in Society Survey sociological theories of deviance, labeling theory and social-conflict theory. Examine the American class system alongside global stratification.
Sex and Gender in Society See how much of a role gender plays in defining individuals and learn about the role of sex in society.
Race and Ethnicity in Society Examine the ways race and ethnicity influence interactions between social minorities and majorities. Study theories used to explain prejudice.
Aging in Society Explore theories of aging and learn about the challenges associated with growing older.
Economics and Politics Discover the links between economics, politics and society by studying such topics as labor markets, the evolution of the economy, forms of government and social power theories.
Social Institutions Study a range of social institutions, including family, religion, schools, and healthcare systems to explore their roles in society.
Social Change Over Time Examine historical migration patterns, the growth of cities, and causes of demographic change. Take a look at crowd behavior along with the types and stages of social movements.