# Substitution method review (systems of equations)

CCSS Math: 8.EE.C.8, 8.EE.C.8b, HSA.REI.C.6

The substitution method is a technique for solving a system of equations. This article reviews the technique with multiple examples and some practice problems for you to try on your own.

## What is the substitution method?

The substitution method is a technique for solving systems of linear equations. Let's walk through a couple of examples.

### Example 1

We're asked to solve this system of equations:

The second equation is solved for $x$, so we can substitute the expression $-y+3$ in for $x$ in the first equation:

Plugging this value back into one of our original equations, say $x = -y +3$, we solve for the other variable:

The solution to the system of equations is $x=-3$, $y=6$.

We can check our work by plugging these numbers back into the original equations. Let's try $3x+y = -3$.

Yes, our solution checks out.

### Example 2

We're asked to solve this system of equations:

In order to use the substitution method, we'll need to solve for either $x$ of $y$ in one of the equations. Let's solve for $y$ in the second equation:

Now we can substitute the expression $2x+9$ in for $y$ in the first equation of our system:

Plugging this value back into one of our original equations, say $y=2x+9$, we solve for the other variable:

The solution to the system of equations is $x=-2$, $y=5$.

*Want to learn more about the substitution method? Check out this video.*