## Elementary Algebra

First, we simplify the two equations: Equation one: $-2x -4 +4y -12 = -34 \\ -2x + 4y = -18$ Equation two: $3x + 12 - 5y -10 = 23 \\ 3x - 5y = 21$ In order to solve this problem, we multiply one or both of the equations by a value that will make one of the variables cancel. We multiply the top equation by 3, and we multiply the bottom equation by 2. Then, we add the two equations to obtain: $12y - 10y = -12 \\ 2y = -12 \\ y =- 6$ We plug in the given value into the top equation and solve for the other variable: $-2x +4(-6) = -18 \\ -2x = 6 \\ x = -3$