2. Fri 10/16 Lesson 3 – 2 Learning Objective: To solve systems algebraically Hw: Pg. 146 #10, 16, 17, 23-39 odd

3. Algebra II

4.  To solve systems by substitution  To solve systems by elimination

5.  0 = 5  Never True!! ◦ No Solution ◦ Parallel Lines  5 = 5  Always True!! ◦ Infinite Solutions ◦ Same Line

6.  Get a variable by itself in one equation  Plug into other equation to solve  Plug solved variable back into one eq’n to solve for other variable  Solution is where the two lines will intersect

7. x – 7y = 11 +7y +7y x = 7y + 11 5(7y + 11) + 4y = - 23 35y + 55 + 4y = - 23 39y = - 78 y = -2 Now plug y = -2 into either equation to solve for x. x – 7(-2) = 11 x + 14 = 11 x = -3 (-3, -2)

8. -2x + y = 3 +2x y = 2x + 3 2x – (2x + 3) = - 6 2x – 2x – 3 = -6 -3 = -6 No Solution! Lines are parallel & will never intersect!

9. 5x + y = -5 -5x y = -5x - 5 6x + 2(-5x – 5) = -10 6x – 10x – 10 = -10 -4x = 0 x = 0 6(0) + 2y = -10 2y = -10 y = - 5 (0, -5)

10.  Pick one variable and get opposite coefficients  Add straight down & solve  Plug solved variable back into one eq’n to solve for other variable  Solution is where the two lines will intersect

11. 5y = 25 y = 5 Since “x” already have opposite coefficients of 4 and -4, just add straight down

12. 3x + 8(3) = 9 3x + 24 = 9 3x = -15 x = -5 15y = 45 y = 3 (-5, 3) (2)( ) (2)

13. 6(2) – 5y = -8 12 – 5y = -8 -5y = -20 y = 4 2x = 4 x = 2 (2, 4) (-1)( ) (-1)

14. Parallel Lines! 0 = -102 No Solution (-3)( ) (-3)

15. Same Line! 0 = 0 Infinite Solutions (-3)( ) (-3)

16. (3)( ) (3) (-4)( ) (-4)

17. 2x + 7(2) = 4 2x + 14 = 4 2x = -10 x = -5 -11y = -22 y = 2 (-5, 2) (2)( ) (2) (-3)( ) (-3)

18. 11. An online photo store charges $0.15/photo plus $2.70 shipping. A local store charges $0.25 with no shipping. a) Write a cost eq’n for each store b) When would it cost the same? c) When do you use online vs. local?

19. Use online store if more than 27 photos. Use local store if less than 27 photos. 0.25x = 0.15x + 2.70 0.10x = 2.70 x = 27 photos would cost both $6.75 Solve by substitution

20.  You work for Alg Comp delivering packages. Alg Comp pays you a flat rate of $9.50 per hour. Geo Comp pays employees $2 per hour plus $3 per delivery. How many deliveries would Geo Comp’s employees have to make in four hours to earn the same pay you earn in a four-hour shift?