When we solve an

equation that has only one variable, we are finding the value for that

variable that makes the

equation true. If our

equation has two variables, there can be infinitely many combinations of numbers that would work. For example, if we have an

equation like

, values of x and y could be 1 and 4, 2 and 3, or any other

combination of numbers.

A

system of equations is when we have more than one

equation and more than one variable. For example:

We refer to this as a

system of equations, meaning that we want x and y values that make BOTH equations true.

There are several ways to solve a

system of equations. This lesson focuses on using matrices to solve a system.

To begin, we must create two matrices from the given

system of equations. One of those matrices is referred to as the

coefficient matrix. It is called the

coefficient matrix because it is created by using the coefficients of the variables involved. So for our system, the

coefficient matrix is:

The second

matrix we will create is called the constant matrix. It is created from the constants on the right

side of the equal signs. In our system, the constant

matrix is:

Now we want to use these matrices to solve our

system of equations. To do so, we will use the calculator, find an inverse, and multiply matrices. If you need help with any of those topics, click on the links below.

Letâ€™s begin by entering

and

into the calculator.

Below is a calculator screen showing that

and

have been entered.

To use these matrices to solve the

system of equations, we need to find the

inverse of

and multiply that answer by

.

By pressing

, we will get answers for x and y that will solve our

system of equations.

This tells us that x = 1 and y = 4.