# PSAT Systems of Equations: Combination/Substitution

Now that you understand the requirements that must be satisfied to solve a system of equations, let’s look at some methods for solving these systems effectively. The two main methods for solving a system of linear equations are substitution and combination (sometimes referred to as elimination by addition).

Substitution is the most straightforward method for solving systems, and it can be applied in every situation. Unfortunately, it is often the longest and most time-consuming route for solving systems of equations as well. To use substitution, solve the simpler of the two equations for one variable, and then substitute the result into the other equation. You could use substitution to answer the following question, but you’ll see that there’s a quicker way: combination.

Combination involves adding the two equations together to eliminate a variable. Often, one or both of the equations must be multiplied by a constant before they are added together. Combination is often the best technique to use to solve a system of equations as it is usually faster than substitution.

Unfortunately, even though most students prefer substitution, problems on the PSAT are often designed to be quickly solved with combination. To really boost your score on Test Day, practice combination as much as you can on Practice Tests and in homework problems so that it becomes second nature.

Work through the Kaplan Method for Math step-by-step to solve this question. The following table shows Kaplan’s strategic thinking on the left, along with suggested math scratchwork on the right.