Question

What is the purpose of using the elimination method?

Answer 1

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`.