1. WARM – UP #2 10/16/15 Fri HW: Pg. 146 #10, 16, 17, 23-39 odd

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

3. LESSON 3 – 2 SOLVING SYSTEMS ALGEBRAICALLY Algebra II

4. LEARNING OBJECTIVE To solve systems by substitution To solve systems by elimination Because I know this!!!

5. SOLUTIONS OF SYSTEMS 0 = 5  Never True!!  No Solution  Parallel Lines 5 = 5  Always True!!  Infinite Solutions  Same Line

6. SOLVE BY SUBSTITUTION Get a variable by itself in one equation (ISOLATE) 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. SOLVE BY SUBSTITUTION 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) Modified/isolated version substitute

8. SOLVE BY SUBSTITUTION -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! Modified/isolated version substitute

9. SOLVE BY SUBSTITUTION 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) Modified/isolated version substitute

10. SOLVE BY ELIMINATION Pick one variable and get opposite coefficients (Ex: 5x & -5x) Line up variables 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. SOLVE BY ELIMINATION 5y = 25 y = 5 Since “x” already have opposite coefficients of 4 and -4, just add straight down

12. SOLVE BY ELIMINATION 3x + 8(3) = 9 3x + 24 = 9 3x = -15 x = -5 15y = 45 y = 3 (-5, 3) (2)( ) (2) Eliminate x (try to get -6x and +6x)

13. SOLVE BY ELIMINATION 6(2) – 5y = -8 12 – 5y = -8 -5y = -20 y = 4 2x = 4 x = 2 (2, 4) (-1)( ) (-1) Eliminate y (try to get -5y and +5y)

14. SOLVE BY ELIMINATION – JUST WATCH Parallel Lines! 0 = -102 No Solution (-3)( ) (-3)

15. SOLVE BY ELIMINATION – JUST WATCH Same Line! 0 = 0 Infinite Solutions (-3)( ) (-3)

16. SOLVE BY ELIMINATION (3)( ) (3) (-4( ) (-4)

17. SOLVE BY ELIMINATION– JUST WATCH 2x + 7(2) = 4 2x + 14 = 4 2x = -10 x = -5 -11y = -22 y = 2 (-5, 2) (2)( ) (2) (-3)( ) (-3)

18. WORD PROBLEM 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. WORD PROBLEM c) Use online store if more than 27 photos. Use local store if less than 27 photos. b) 0.25x = 0.15x + 2.70 0.10x = 2.70 x = 27 photos would cost both $6.75 Solve by substitution

20. TICKET OUT THE DOOR 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?

21. ASSIGNMENT: PG. 146 #10, 16, 17,23-39 ODD