Problem: Solve x + 2 y = − 6 ; 3 x + 8 y = − 20 Steps: I will solve your system by substitution. (You can also solve this system by elimination.) x + 2 y = − 6 ; 3 x + 8 y = − 20 Step: Solve x + 2 y = − 6 for x: x + 2 y + − 2 y = − 6 + − 2 y (Add -2y to both sides) x = − 2 y − 6 Step: Substitute − 2 y − 6 for x in 3 x + 8 y = − 20 : 3 x + 8 y = − 20 3 ( − 2 y − 6 ) + 8 y = − 20 2 y − 18 = − 20 (Simplify both sides of the equation) 2 y − 18 + 18 = − 20 + 18 (Add 18 to both sides) 2 y = − 2 2 y 2 = − 2 2 (Divide both sides by 2) y = − 1 Step: Substitute − 1 for y in x = − 2 y − 6 : x = − 2 y − 6 x = ( − 2 ) ( − 1 ) − 6 x = − 4 (Simplify both sides of the equation) Answer: x = − 4 and y = − 1
