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
, values of x and y could be 1 and 4, 2 and 3, or any other combination
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
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
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
into the calculator.
Below is a calculator screen showing that
have been entered.
To use these matrices to solve the system
of equations, we need to find the inverse
and multiply that answer by
, we will get answers for x and y that will solve our system
This tells us that x = 1 and y = 4.