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How to solve systems of equations by Elimination

Step by step tutorial for systems of linear equations (in 2 variables)

on Solving by Elimination

What is the Elimination Method?

It is one way to solve a system of equations.

The basic idea is if you have 2 equations, you can sometimes do a single operation and then add the 2 equations in a way that eleiminates 1 of the 2 variables as the example that follows shows.

elimination method example
In this system, if we add the 2 equations together, the $$ \red{- 10y} $$ and $$ \red{10y} $$ will eliminate each other! And that is the crux of what the rest of this page will explore.

Elimination Example 1

$$ y = x + 1 \\ y = -x $$

elimination method

Practice Problems

Problem 1
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Problem 2
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Problem 3
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Back to Systems of Equations Next to Solve by Substitution