What is the purpose of using the elimination method?

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

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

##2x+3y=1## ##-2x+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:

##4y=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##.