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7.2: Solving Linear Systems by Substitution Integrated Math 2 Steps for Substitution (1) Pick the easiest equation that has a 1x or 1y, solve the equation for that variable (2) Plug the expression on the right into the equation that has not been used for the appropriate variable - Make sure the same variable is in the equation (3) Solve the equation for the first variable (4) Plug the solution back into an equation to find the other variable - Any equation will work!!! Solving for y first x y 4 4 x y 1 x+y=4 -x -x . y = -x + 4 Plug the expression in and solve: 4x + y = 1 4x + 1(-x+4) = 1 4x + -x + 4 = 1 3x + 4 = 1 -4 -4 3x = -3 3 3 x = -1 Plug x back in to find y: y = -x + 4 = -(-1) + 4 =5 So the final answer is (-1, 5) (This is the exact point the lines would cross at on a graph) Example 2: Solve for x first x y 4 4 x y 1 x+y=4 -y -y x = -y + 4 Plug in the expression and solve: 4x + y = 1 4(-y+4) + y = 1 -4y + 16 + y = 1 -3y + 16 = 1 -16 -16 -3y = -15 -3 -3 y=5 Plug y back in to find x: x = -y + 4 = -(5) + 4 = -1 The answer is still (-1, 5)