How to Solve Systems Using Linear Combinations

By Society & Culture & Entertainment Last updated Tuesday, June/04/2024

1). Rearrange, if necessary, the equations in your system so the variables line up. For instance, arrange both equations so the variables are in order such as x + y = 0. The variables must line up in order to cancel out.
2). Multiply one or both equations by a constant if no variables automatically cancel out from Step 1. The goal is to multiply one or both equations so one variable will be eliminated when added together.
3). Add your equations together to form a new equation.
4). Solve your new equation for which ever variable is remaining.
5). Substitute the result from Step 4 into one of your original equations to solve for the second variable.