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# Integrated Math 2 Section 8-7

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Systems of Inequalities

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• ### Integrated Math 2 Section 8-7

1. 1. SECTION 8-7 Systems of Inequalities
2. 2. ESSENTIAL QUESTIONS • How do you write a system of linear inequalities for a given graph? • How do you graph the solution set of a system of linear inequalities? • Where you’ll see this: • Sports, entertainment, retail, ﬁnance
3. 3. EXAMPLE 1 Graph the following linear inequalities on separate coordinates, then again on the same coordinates. y < 2x + 3 y ≥ −3x + 4
4. 4. EXAMPLE 1 Graph the following linear inequalities on separate coordinates, then again on the same coordinates. y < 2x + 3 y ≥ −3x + 4
5. 5. EXAMPLE 1 Graph the following linear inequalities on separate coordinates, then again on the same coordinates. y < 2x + 3 y ≥ −3x + 4
6. 6. EXAMPLE 1 Graph the following linear inequalities on separate coordinates, then again on the same coordinates. y < 2x + 3 y ≥ −3x + 4
7. 7. EXAMPLE 1 Graph the following linear inequalities on separate coordinates, then again on the same coordinates. y < 2x + 3 y ≥ −3x + 4
8. 8. EXAMPLE 1 Graph the following linear inequalities on separate coordinates, then again on the same coordinates. y < 2x + 3 y ≥ −3x + 4
9. 9. EXAMPLE 1 Graph the following linear inequalities on separate coordinates, then again on the same coordinates. y < 2x + 3 y ≥ −3x + 4
10. 10. EXAMPLE 1 Graph the following linear inequalities on separate coordinates, then again on the same coordinates. y < 2x + 3 y ≥ −3x + 4
11. 11. EXAMPLE 1 Graph the following linear inequalities on separate coordinates, then again on the same coordinates. y < 2x + 3 y ≥ −3x + 4
12. 12. EXAMPLE 1 Graph the following linear inequalities on separate coordinates, then again on the same coordinates.
13. 13. EXAMPLE 1 Graph the following linear inequalities on separate coordinates, then again on the same coordinates.
14. 14. EXAMPLE 1 Graph the following linear inequalities on separate coordinates, then again on the same coordinates.
15. 15. EXAMPLE 1 Graph the following linear inequalities on separate coordinates, then again on the same coordinates.
16. 16. EXAMPLE 2 Write a system of linear inequalities for the graph shown.
17. 17. EXAMPLE 2 Write a system of linear inequalities for the graph shown.  y ≥ −4x + 6   1 y < x − 3  2
18. 18. EXAMPLE 3 Matt Mitarnowski was planning a wedding reception that will last at least 4 hours. The couple wants to hire a band that charges \$300 per hour and a DJ that charges \$150 per hour. They want to keep the music expenses under \$1200. The band and DJ charge by the whole hour only. a. Write a system of linear inequalites that models the situation.
19. 19. EXAMPLE 3 Matt Mitarnowski was planning a wedding reception that will last at least 4 hours. The couple wants to hire a band that charges \$300 per hour and a DJ that charges \$150 per hour. They want to keep the music expenses under \$1200. The band and DJ charge by the whole hour only. a. Write a system of linear inequalites that models the situation. x = DJ, y = band
20. 20. EXAMPLE 3 Matt Mitarnowski was planning a wedding reception that will last at least 4 hours. The couple wants to hire a band that charges \$300 per hour and a DJ that charges \$150 per hour. They want to keep the music expenses under \$1200. The band and DJ charge by the whole hour only. a. Write a system of linear inequalites that models the situation. x = DJ, y = band Time:
21. 21. EXAMPLE 3 Matt Mitarnowski was planning a wedding reception that will last at least 4 hours. The couple wants to hire a band that charges \$300 per hour and a DJ that charges \$150 per hour. They want to keep the music expenses under \$1200. The band and DJ charge by the whole hour only. a. Write a system of linear inequalites that models the situation. x = DJ, y = band Time: x + y ≥ 4
22. 22. EXAMPLE 3 Matt Mitarnowski was planning a wedding reception that will last at least 4 hours. The couple wants to hire a band that charges \$300 per hour and a DJ that charges \$150 per hour. They want to keep the music expenses under \$1200. The band and DJ charge by the whole hour only. a. Write a system of linear inequalites that models the situation. x = DJ, y = band Time: x + y ≥ 4 Money:
23. 23. EXAMPLE 3 Matt Mitarnowski was planning a wedding reception that will last at least 4 hours. The couple wants to hire a band that charges \$300 per hour and a DJ that charges \$150 per hour. They want to keep the music expenses under \$1200. The band and DJ charge by the whole hour only. a. Write a system of linear inequalites that models the situation. x = DJ, y = band Time: x + y ≥ 4 Money: 150x + 300y <1200
24. 24. EXAMPLE 3 Matt Mitarnowski was planning a wedding reception that will last at least 4 hours. The couple wants to hire a band that charges \$300 per hour and a DJ that charges \$150 per hour. They want to keep the music expenses under \$1200. The band and DJ charge by the whole hour only. a. Write a system of linear inequalites that models the situation. x = DJ, y = band x + y ≥ 4 Time: x + y ≥ 4  150x + 300y <1200 Money: 150x + 300y <1200
25. 25. EXAMPLE 3 b. Solve the system by graphing. x + y ≥ 4  150x + 300y <1200
26. 26. EXAMPLE 3 b. Solve the system by graphing. x + y ≥ 4  150x + 300y <1200 x+y≥4
27. 27. EXAMPLE 3 b. Solve the system by graphing. x + y ≥ 4  150x + 300y <1200 x+y≥4 −x −x
28. 28. EXAMPLE 3 b. Solve the system by graphing. x + y ≥ 4  150x + 300y <1200 x+y≥4 −x −x y ≥ −x + 4
29. 29. EXAMPLE 3 b. Solve the system by graphing. x + y ≥ 4  150x + 300y <1200 x+y≥4 150x + 300y <1200 −x −x y ≥ −x + 4
30. 30. EXAMPLE 3 b. Solve the system by graphing. x + y ≥ 4  150x + 300y <1200 x + y ≥ 4 150x + 300y <1200 −x −x −150x −150x y ≥ −x + 4
31. 31. EXAMPLE 3 b. Solve the system by graphing. x + y ≥ 4  150x + 300y <1200 x + y ≥ 4 150x + 300y <1200 −x −x −150x −150x y ≥ −x + 4 300y < −150x +1200
32. 32. EXAMPLE 3 b. Solve the system by graphing. x + y ≥ 4  150x + 300y <1200 x + y ≥ 4 150x + 300y <1200 −x −x −150x −150x y ≥ −x + 4 300y < −150x +1200 300 300
33. 33. EXAMPLE 3 b. Solve the system by graphing. x + y ≥ 4  150x + 300y <1200 x + y ≥ 4 150x + 300y <1200 −x −x −150x −150x y ≥ −x + 4 300y < −150x +1200 300 300 1 y <− x+4 2
34. 34. EXAMPLE 3 b. Solve the system by graphing. x + y ≥ 4  150x + 300y <1200 x + y ≥ 4 150x + 300y <1200 −x −x −150x −150x y ≥ −x + 4 300y < −150x +1200 300 300 1 y <− x+4 2
35. 35. EXAMPLE 3 b. Solve the system by graphing. x + y ≥ 4  150x + 300y <1200 x + y ≥ 4 150x + 300y <1200 −x −x −150x −150x y ≥ −x + 4 300y < −150x +1200 300 300 1 y <− x+4 2
36. 36. EXAMPLE 3 b. Solve the system by graphing. x + y ≥ 4  150x + 300y <1200 x + y ≥ 4 150x + 300y <1200 −x −x −150x −150x y ≥ −x + 4 300y < −150x +1200 300 300 1 y <− x+4 2
37. 37. EXAMPLE 3 b. Solve the system by graphing. x + y ≥ 4  150x + 300y <1200 x + y ≥ 4 150x + 300y <1200 −x −x −150x −150x y ≥ −x + 4 300y < −150x +1200 300 300 1 y <− x+4 2
38. 38. EXAMPLE 3 b. Solve the system by graphing. x + y ≥ 4  150x + 300y <1200 x + y ≥ 4 150x + 300y <1200 −x −x −150x −150x y ≥ −x + 4 300y < −150x +1200 300 300 1 y <− x+4 2
39. 39. EXAMPLE 3 b. Solve the system by graphing. x + y ≥ 4  150x + 300y <1200 x + y ≥ 4 150x + 300y <1200 −x −x −150x −150x y ≥ −x + 4 300y < −150x +1200 300 300 1 y <− x+4 2
40. 40. EXAMPLE 3 b. Solve the system by graphing. x + y ≥ 4  150x + 300y <1200 x + y ≥ 4 150x + 300y <1200 −x −x −150x −150x y ≥ −x + 4 300y < −150x +1200 300 300 1 y <− x+4 2
41. 41. EXAMPLE 3 b. Solve the system by graphing. x + y ≥ 4  150x + 300y <1200 x + y ≥ 4 150x + 300y <1200 −x −x −150x −150x y ≥ −x + 4 300y < −150x +1200 300 300 1 y <− x+4 2
42. 42. EXAMPLE 3 b. Solve the system by graphing. x + y ≥ 4  150x + 300y <1200 x + y ≥ 4 150x + 300y <1200 −x −x −150x −150x y ≥ −x + 4 300y < −150x +1200 300 300 1 y <− x+4 2
43. 43. EXAMPLE 3 b. Solve the system by graphing.
44. 44. EXAMPLE 3 b. Solve the system by graphing. (1, 3), (2, 2), (2, 3), (3, 1), (4, 1), (5, 1)
45. 45. HOMEWORK
46. 46. HOMEWORK p. 364 #1-21 odd, 23-30 all “Try to learn something about everything and everything about something.” - Thomas H. Huxley