5.2 Substitution Try this one: x = 4y y = 5x 4x – y = 75 2x + 3y = 34 (2, 10) x = 4y 4x – y = 75 4(4y) – y = 75 16y – y = 75 15y = 75 y = 5 x = 4(5) x = 20 Ordered Pair (20, 5)

Substitution Method for solving 2 equation with 2 variables 1. x + y = 15 2. x – y = 9 Get one variable by itself so that you can use it to substitute. Solve the second equation for x = 9 + y Plug 9 + y into the first equation for x. (9 + y) + y = 15 9 + 2y = 15 2y = 6 y = 3 x = 9 + 3 x = 12 (12, 3)

2x + 2y = 8 x + y = -2 x = -2 – y 2(-2 – y) + 2y = 8 -4 – 2y + 2y = 8 -4 = 8 FALSE!! Answer: No Solution x – 2y = 3 4x – 8y = 12 x = 3 + 2y 4(3 + 2y) – 8y = 12 12 + 8y – 8y = 12 12 = 12 TRUE Answer: Infinitely Many Solutions

Toshiro weighs 12 pounds less than Steve Toshiro weighs 12 pounds less than Steve. The sum of their weights is 118 pounds. How much does Steve weigh? How much does Toshiro weigh? Toshiro = T Steve = S T = S – 12 T + S = 118 S – 12 + S = 118 2S – 12 = 118 2S = 130 S = 65 pounds T = 65 – 12 T = 53 pounds

Your Turn y = 6x 2x + 3y = -20 x – 2y = 3 3x – 6y = 9 3x + y = 12 Answer: (-1, -6) x – 2y = 3 3x – 6y = 9 x + 14y = 84 2x – 7y = -7 y = 2x + 6 2x – y = 2 Answer: Infinitely Many Answer: (7, -9) Answer: (14, 5) Answer: No Solution

Try These page 263 #1, 3, 5 1. (5, -1) 3. No Solution 5. (-2, 3)