# Elimination method review (systems of linearÂ equations)

CCSS Math: HSA.REI.C.6

The elimination method is a technique for solving systems of linear equations. This article reviews the technique with examples and even gives you a chance to try the method yourself.

## What is the elimination method?

The elimination 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:

We notice that the first equation has a $7x$ term and the second equation has a $-7x$ term. These terms will cancel if we add the equations togetherâ€”that is, we'll

*eliminate*the $x$ terms:Solving for $y$, we get:

Plugging this value back into our first equation, we solve for the other variable:

The solution to the system is $x=\blueD{-1}$, $y=\goldD{1}$.

We can check our solution by plugging these values back into the the original equations. Let's try the second equation:

Yes, the solution checks out.

*If you feel uncertain why this process works, check out this intro video for an in-depth walkthrough.*

### Example 2

We're asked to solve this system of equations:

We can multiply the first equation by $-4$ to get an equivalent equation that has a $\purpleD{-16x}$ term. Our new (but equivalent!) system of equations looks like this:

Adding the equations to eliminate the $x$ terms, we get:

Solving for $y$, we get:

Plugging this value back into our first equation, we solve for the other variable:

The solution to the system is $x=\blueD{5}$, $y=\goldD{0}$.

*Want to see another example of solving a complicated problem with the elimination method? Check out this video.*

## Practice

*Want more practice? Check out these exercises:*