I CAN solve systems of equations with substitution

I CAN. . . ~solve systems of equations with substitution. LESSON 7 -2 B

WARM-UP Solve these two systems by graphing.

EXAMPLE #1 2(2 – y) + 2 y = 8 4 – 2 y + 2 y = 8 4=8 This is FALSE so that means……. ? No solution (parallel lines)

EXAMPLE #2 c – 4 d = 1 +4 d Hint: Get c by itself. c = 4 d + 1 2(4 d + 1) – 8 d = 2 8 d + 2 – 8 d = 2 0+2=2 Infinitely many = This is TRUE so that means……. ? Same line

SUMMARY If your variables “cancel out” and the result is: TRUE: such as – 5 = – 5 False: such as 5 = 8 Infinitely many Solution: ____________ Solution: No solutions SAME line Type of line: ______ Type of Paralle l line:

YOUR TURN y=x+4 3 x + 2(x + 4) = 18 3 x + 2 x + 8 = 18 y=2+4 y=6 5 x + 8 = 18 5 x = 10 x=2 Solution: (2, 6)

YOUR TURN 4 x + 2(– 2 x + 3) = 6 4 x – 4 x + 6 = 6 6=6 Infinitely many = This is TRUE so that means……. ? Same line

EXAMPLE #3 Sue had two tests on Monday (history and biology). Her biology score was 12 points higher than her history score. The total of her two scores was 154. What was her biology test score? b = 12 + h b + h = 154 b = 12 + 71 b = 83 12 + h = 154 12 + 2 h = 154 – 12 2 h = 142 h = 71

EXAMPLE #4 Dan bought two new games for his Wii. Super Mario Brothers cost twice as much as Lego Star Wars. The total for both games was $72. What does Lego Star Wars cost? m = 2 L m + L = 72 2 L+ L = 72 3 L = 72 L = 24

EXAMPLE #5 Lucy is selling girl scout cookies. She sells 4 times as many boxes of Caramel Delites as Thin Mints. Caramel Delites cost $4 per box and Thin Mints cost $3. 50 per box. She makes a total of $156. How many boxes of Caramel Delites did she sell? c = 4 m 19. 50 m = 156 4 c + 3. 50 m = 156 m=8 4(4 m) + 3. 50 m = 156 16 m + 3. 50 m = 156 c = 4(8) c = 32

ARE YOU A MASTER? What does an infinitely many solutions mean? What does a no solution mean?