What does the elimination method do in solving systems of equations?

The elimination method is a technique used to solve systems of equations by systematically eliminating one of the variables, allowing for a simpler equation to work with. When applying this method, you can manipulate the equations—by adding or subtracting them—to eliminate one variable so that you can solve for the other variable directly.

For example, if you have a system of two equations, you can multiply one or both of the equations by suitable values to align the coefficients of one of the variables. When you add or subtract these adjusted equations, one variable is effectively eliminated. This leaves you with a single equation in one variable, which can then be solved easily.

After finding the solution for one variable, you can substitute it back into one of the original equations to solve for the other variable. This method is particularly effective for linear equations and provides a clear, systematic approach to finding the solution to the system.