That system of equations is being solved by elimination, eliminating 'y', leading to a solution for 'x'.  Once 'x' is solved for then 'y' can be solved for using either equation [unless, of course, the graphs do not touch each other]. 

Some linear systems can be more directly controlled through Algebrator.  To help you clearly understand our desktop software and how appropriate it may be for your needs, please use one of the following links to obtain a free trial of the program:

Windows: http://www.softmath.com/tr/alg51win-tr-en.exe

Mac: http://www.softmath.com/tr/alg51mac-tr-en.dmg

It is important to understand that anytime you are solving a system of equations you are answering the basic question "Do the graphs of these equations touch?". They may touch in one point (one solution), no points (no solutions) or an infinite number of points (i.e. the equations define the same line).