Methods of Solving Systems Of Equations Whenever there is something to do, there are always many ways to do it. This hold true with solving systems of equations. To solve the systems, there are five main methods to use. These methods include solving by graphing, substitution, linear combination, inverse matrices, and Cramer’s Rule. Solving by graphing is one of the simplest ways to solve an equation. In order to solve this way, the equations in the system need to be in slope intercept form. After the equations are in slope intercept form, you can plot them easily using the slope and y intercept. Once the lines are graphed, one of three th