Graphing: Graphing is the best method to use when introducing a new student to solving systems of two equations in two variables, because it gives them a visiual to recognize what they are looking for. Graphing is less exact and often takes more time than the other methods. I only recommend graphing to find a solution if the problem comes with a graph already drawn and the intersection appears to be on an exact coordinate.
Substitution: Substition gives that advantage of having an equation alrady written for the second variable when you find the first one. Substitution is best used when one (or both) of the equations is already solved for one of the variables. It also works well if one of the variables has a coefficient of 1.
Elimination: Elimination is the method that I use almost every time. If you are not sure which method to use, I recommend that you use elimination. Elimination is best used when both equations are in standard form (Ax + By = C). Elimination is also the best method to use if all of the variables have a coefficient other than 1.
