Which method involves adding equations to cancel out a variable when solving a system?

• A. Substitution
• B. Graphing
• C. Factoring
• D. Elimination

Answer: (D)

Elimination is a way to solve a system by canceling one variable through addition. You choose a variable to eliminate, multiply the equations by numbers that make that variable’s coefficients opposite, then add the equations to remove it. The result is an equation with a single variable, which you can solve, and then you back-substitute to find the other variable.

For example, with x + y = 3 and x − y = 1, the y terms cancel when you add the equations, giving 2x = 4, so x = 2. Then substitute back to find y (2 + y = 3, so y = 1).

Other methods solve systems in different ways: substitution solves one equation for a variable and plugs it into the other; graphing looks for the intersection point of the two lines; factoring is used when the equations involve factors of polynomials to find roots.