Which method is typically used to eliminate a variable when solving by the elimination method?

In the elimination method for solving systems of equations, the goal is to eliminate one of the variables by combining the equations in such a way that one variable drops out. This is typically achieved by adding or subtracting the equations after possibly adjusting them (through multiplication or other means) to ensure that the coefficients of one of the variables are opposites or the same.

When adding both equations, if the coefficients of one variable are equal and opposite, that variable will cancel out, leading to a new simplified equation with only one variable. By solving this new equation for the remaining variable, you can then substitute back to find the value of the eliminated variable in the context of the original equations. This process is foundational in the elimination method because it allows for a straightforward path to finding solutions to systems of equations.