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Solving Multiplication Equations with Two or More Variables

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  • 0:01 A Multiplication Problem
  • 0:35 The Equations
  • 1:06 Solving the Equations
  • 3:39 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 video lesson, you should be able to solve multiplication problems with more than one variable. Learn how many equations you will need to solve your problem. Learn how the number of variables determines the number of equations.

A Multiplication Problem

An important skill to have in your math toolkit is that of solving multiplication equations. In this video lesson, you will learn how to solve multiplication problems with two or more variables. These are math problems that involve the multiplication operator and more than one unknown value. It is these unknown values that you need to solve for. Here is an example of a multiplication problem that you might come across:

xy = 50
2x = y

Learning how to solve these kinds of problems will be a very useful skill for you as you progress in your math classes and as you come across problems at work and in life.

The Equations

Do you notice something interesting about the problem that you just saw?

xy = 50
2x = y

That's right. There is more than one equation in this problem. This is because the problem has more than one variable. An important rule that you need to remember for problems of this type is that you need to have one equation for every variable that you have. So, if you have four variables or four unknown values in your problem, then you will need four equations in your problem to be able to solve it.

Solving the Equations

So, how do you solve these equations? The way to solve these problems is first to solve one of the equations for one of the variables. Then you use this information to plug it into the other equation. The goal of plugging into another equation is to arrive at an equation with just one variable. If you have more than two variables, then you go ahead and solve for several of the equations. The choice of which variable to solve for depends on the equation that you will be plugging into. You need to look at the equation to see which variables you need to plug in so that you end up with an equation with just one variable.

Looking at your current problem, you see that you can use the second equation, which is already solved for the variable y, and plug it into the first equation. When you do this, you end up with an equation with just one variable, the x variable:

x*(2x) = 50
2x^2 = 50

This is an equation that you can easily solve by using the equation solving skills you already have. To solve for the variable, you isolate the variable. For this particular equation, you first divide by 2 on both sides. Then you take the square root of both sides to get the x by itself. The square root cancels out the square root.

2x^2/2 = 50/2
x^2 = 25
sqrt(x^2) = sqrt(25)
x = 5

The x equals 5. Now, to solve for the y, you can use the second equation and plug in what the x equals.

2x = y
2*(5) = y
10 = y

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