Which method involves manipulating equations to eliminate a variable?

The method that involves manipulating equations to eliminate a variable is known as elimination. This technique is used primarily when solving systems of linear equations. In the elimination method, you add or subtract the equations to cancel out one of the variables, making it possible to solve for the remaining variable.

For example, if you have two linear equations, you can align them such that adding or subtracting them will lead to the cancellation of one of the variables. This simplifies the problem and allows for a more straightforward solution process as you can focus solely on the one variable left.

Other methods mentioned involve different approaches. Substitution, for instance, involves solving one equation for one variable and then substituting that expression into the other equation. Fraction reduction pertains to simplifying fractions and does not directly relate to the manipulation of equations. Graphing involves visually representing equations on a coordinate plane and finding points of intersection, which is also a different approach from directly manipulating the equations algebraically. Thus, elimination stands out as the method specifically focused on removing variables through algebraic manipulation.