# What is the purpose of using the elimination method?

Dec 11, 2014

The elimination method reduces the problem to solving a one variable equation.

For example, look at the following system of two variables:

$2 x + 3 y = 1$
$- 2 x + y = 7$

It is relatively difficult to determine the values of $x$ and $y$ without manipulating the equations. If one adds the two equations together, the $x$s cancel out; the $x$ is eliminated from the problem. Hence it is called the "elimination method."

One ends up with:

$4 y = 8$

From there, it is trivial to find $y$, and one can simply plug the value of $y$ back into either equation to find $x$.