Main content

## Algebra basics (ASL)

### Course: Algebra basics (ASL) > Unit 5

Lesson 2: Elimination method for systems of equations (ASL)- Systems of equations with elimination: King's cupcakes
- Systems of equations with elimination: x-4y=-18 & -x+3y=11
- Systems of equations with elimination
- Systems of equations with elimination: potato chips
- Systems of equations with elimination (and manipulation)
- Systems of equations with elimination challenge
- Why can we subtract one equation from the other in a system of equations?
- Elimination method review (systems of linear equations)

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Elimination method review (systems of linear equations)

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 7, x term and the second equation has a minus, 7, x term. These terms will cancel if we add the equations together—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, equals, start color #11accd, minus, 1, end color #11accd, y, equals, start color #e07d10, 1, end color #e07d10.

We can check our solution by plugging these values back into 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 minus, 4 to get an equivalent equation that has a start color #7854ab, minus, 16, x, end color #7854ab 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, equals, start color #11accd, 5, end color #11accd, y, equals, start color #e07d10, 0, end color #e07d10.

*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:*

## Want to join the conversation?

No posts yet.