When you are solving a system of two equations with two variables then what you are doing is actually looking for the points of intersection of the corresponding graphs.
These intersects can often be found by:

• combining both equations such that you end up with one equation with just one variable;

• reorganising both equations such that you can enter them in your graphing caclulator, and letting the machine find the required intersects.

When you choose to combine the equations you can use:

• substitution:
  You express one variable in one of the equations in terms of the other, and then substitute this expression for the variable in the other equation.

• the balancing method:
  You add up the left and right sides of the two equations. Before you do so, you have to make sure that one of the two variables will be eliminated when you do this addition (usually by multiplying one or both equations with a suitable factor).