Solving Subtraction Equations with Two or More Variables

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  • 0:01 A Subtraction Problem
  • 1:02 Finding the First Solution
  • 2:20 Finding the Other Solutions
  • 3:15 Example
  • 5:50 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this lesson, you'll be able to solve subtraction problems that involve more than one variable and more than one equation. Learn what steps you need to take and how to work with your equations.

A Subtraction Problem

In this lesson, we'll talk about solving subtraction problems that have more than one variable. These are math problems that involve the subtraction operation and that have two or more unknown values. These are a bit different than our usual subtraction problems that have just one variable and one equation. These problems have more than one equation. For every unknown value that we have, or for every variable that we have, we will have one equation. So, if we have three unknown variables, then we will have three equations. If we have five variables, then we will have five equations. The most common problems that you will solve for will have two or three variables. The more variables that you have, the more complicated the math gets. Solving for two or three variables is plenty when working with just pen and paper. An example of a problem that we might see would be this:

x - y = 8

x - 2y = 6

Finding the First Solution

To solve these types of problems, we need to first take a look at the problem as a whole. What we need to do is to first solve for a few of our variables. We then use this information to plug into one of the equations. The goal here is to create an equation with just one variable. This way we can solve for that variable. After that, we can go ahead and solve for the other variables.

Let's take a look at finding the solution to the first variable. Looking at our equations, at our problem as a whole, we see that if we solve the second equation for x, we can plug that information into the first equation. This leaves us with an equation with just one variable. That is something we can easily solve for.

Solving the second equation for x gives us this:

x - 2y = 6

x - 2y + 2y = 6 + 2y

x = 6 + 2y

Plugging this into the first equation for x and solving, gives us the answer for y:

x - y = 8

(6 + 2y) - y = 8

6 + y = 8

6 + y - 6 = 8 - 6

y = 2

Finding the Other Solutions

Now that we've found the answer to one of our variables, we can now use this information to help us find the answer to the other variables. We do this by plugging in our answer for the variable into the other equations. We see that we have already solved for x, so we can use this equation to find out what x equals by plugging in y = 2.

x = 6 + 2y

x = 6 + 2 * 2

x = 6 + 4

x = 10

And we are done! Our complete answer is x = 10 and y = 2.

If we had a problem with more than two variables, we would solve more equations for the other variables. Our goal is still the same. We still want to create one equation that contains just one variable. After finding the answer to this one variable, we can then plug that answer into the other equations to find our complete answer.


Let's take a look at another example:

x - y - z = 5

x - y = 10

x - z = 15

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