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.