Now let's move into the next technique for solving systems of equations.  As we illustrated in the example the method of substitution will frequently force us to deal with fractions, which adds to the probability of mistakes. This second method will not have this difficulty.  Well, that's not totally true. If fractions are going illustrated they will only illustrates in the final step and they will only show up if the solution contains fractions.

This second technique is called the method of elimination.  In this technique we multiply one or both of the equations by appropriate numbers (i.e. multiply every term in the equation by the number) so that one of the variables will have the similar coefficient along with opposite signs. Then next step is to summing up the two equations together.  Because one of the variables had the same coefficient with opposite signs it will be eliminated when we add the two equations. The result will be single equation which we can solve for one of the variables.  Once this is done substitute this answer back into one of the original equations.