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.

An old video where Sal introduces the elimination method for systems of linear equations. Created by Sal Khan.

In some cases, we need to slightly manipulate a system of equations before we can solve it using the elimination method. See how it's done in this video.

Which of these strategies would eliminate a variable in the system of equations? The first choice says multiply the bottom equation by two, then add the equations.

Solve systems of equation with one-step elimination (e.g., x-values or y-values cancel each other out).

Now what we're gonna do is find an X and Y pair that satisfies both of these equations. That's what solving the system actually means. As you might already have seen, there's a bunch of X and Y pairs …

Every time you multiply or divide a term of an equation, you have to do the same to the other terms, and to the other side of the equation. In your example (6/3)x+2x=13, we would do the same, multiplying …

This isn't a big deal, but when you get into higher classes, you want eliminate these minor mistakes. So I'd recommend reading the problem fully, and looking at each step after you do it, to see if it makes …

Sal explains how we can find the inverse of a 3x3 matrix using Gaussian elimination.

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.