The Elimination Method is a powerful and brutal way to solve a system of equations. The goal: make a variable disappear.

Step 1: The Lineup. Make sure both equations are in standard form (Ax + By = C) and stacked neatly on top of each other.

Step 2: The Target. Look at the coefficients of x and y. Your goal is to make one pair into opposites (like -5 and +5).

Step 3: The Adjustment. If you don't have opposites, you must multiply one or both entire equations to create them.

For example, if you have 2x and 3x, you could multiply the first equation by 3 and the second by -2 to get 6x and -6x.

Step 4: The Elimination. Add the two equations together, column by column. If you did it right, one variable will be eliminated, adding to zero.

You are now left with a simple, one-variable equation. Solve it.

Step 5: The Resurrection. Take the value you just found and plug it back into either of the original equations to find the second variable.

This method is often faster and cleaner than substitution, especially when none of the variables have a coefficient of 1.

Stack 'em, find a target, create opposites, and eliminate. It is a warrior's path to the solution.