Solving by Addition

Solving by the addition method means scaling equations until one variable's coefficients are opposites, adding to eliminate it, solving, back-substituting, and checking the pair in both originals.

Solve 2x + 3y = 12 with 4x − 3y = 6. The y-coefficients, 3 and −3, are opposites already — no scaling needed. Add: 6x = 18, so x = 3. Back-substitute into the first: 6 + 3y = 12, so y = 2. Check the pair (3, 2) in both originals: 6 + 6 = 12 and 12 − 6 = 6. When no coefficients cooperate, multiply one or both equations first — scaling an equation by a nonzero constant changes nothing about its solutions, which is Video 133's both-sides law wearing system clothes.