This document describes the addition/subtraction method for solving systems of linear equations algebraically. It involves eliminating one variable by adding or subtracting equations such that the coefficients of the variable you want to eliminate are the same or negatives of each other. Then the resulting single equation can be solved for the eliminated variable. The method is demonstrated by solving the systems (1) x - 2y = -9, x + 3y = 16 and (2) 2x - y = 9, 3x + 4y = -14, obtaining the solutions (1, 5) and (unknown).