Math 1050 Blog

The methods of elimination and substitution solve systems of equations with two variables.  In elimination, the key step in this method is to obtain, for one or more of the variables, coefficients that differ only in sign so that adding the equations eliminates the variable.  By eliminating one one or more you can receive a single equation in which you can then back substitute that answer into the other equation to find both variables.

In substitution, you perform the following steps.  You first solve one of the equations for one variable in terms of the other.  You then substitute the expression found in step one into the other equation to obtain an equation in one variable.  After that solve the equation in step two.  Back substitute the value(s) obtained in step three into the expression obtained in step one to find the value(s) if the other variable.  Last, check that each solution satisfies both of the original equations.