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Solving Systems of Equations with Matrices I
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. Let’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.

Examples
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S Taylor

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