Its important to separate your goal from your methods.

In this case, it appears you want to find what is essentially the intersection of two lines. ( Linear equations can be graphically presented as lines.)

In this case, there are several methods.

One is to reduce the equations such that you can set the equations equal to each other.

Another is to subtract them from each other.

Both are really the same thing.

This is a great site for Algebra.

http://www.mathwords.com/index_algebra.htm