Int Math 2 Section 8-7

1. SECTION 8-7 Systems of Inequalities

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. EXAMPLE 1 Graph the following linear inequalities on separate coordinates, then again on the same coordinates. y < 2x + 3 y ≥ −3x + 4

12. EXAMPLE 1 Graph the following linear inequalities on separate coordinates, then again on the same coordinates.

16. EXAMPLE 2 Write a system of linear inequalities for the graph shown.

17. EXAMPLE 2 Write a system of linear inequalities for the graph shown.  y ≥ −4x + 6   1 y < x − 3  2

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 inequalities that models the situation.

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 inequalities that models the situation. x = DJ, y = band

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 inequalities that models the situation. x = DJ, y = band Time:

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 inequalities that models the situation. x = DJ, y = band Time: x + y ≥ 4

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 inequalities that models the situation. x = DJ, y = band Time: x + y ≥ 4 Money:

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 inequalities that models the situation. x = DJ, y = band Time: x + y ≥ 4 Money: 150x + 300y <1200

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 inequalities that models the situation. x = DJ, y = band x + y ≥ 4 Time: x + y ≥ 4  150x + 300y <1200 Money: 150x + 300y <1200

25. EXAMPLE 3 b. Solve the system by graphing. x + y ≥ 4  150x + 300y <1200

26. EXAMPLE 3 b. Solve the system by graphing. x + y ≥ 4  150x + 300y <1200 x+y≥4

27. EXAMPLE 3 b. Solve the system by graphing. x + y ≥ 4  150x + 300y <1200 x+y≥4 −x −x

28. EXAMPLE 3 b. Solve the system by graphing. x + y ≥ 4  150x + 300y <1200 x+y≥4 −x −x y ≥ −x + 4

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. 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. 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. 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. 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. EXAMPLE 3 b. Solve the system by graphing.

44. EXAMPLE 3 b. Solve the system by graphing. (1, 3), (2, 2), (3, 1), (3, 2), (4, 1), (5, 1)

45. EXAMPLE 3 b. Solve the system by graphing. (1, 3), (2, 2), (3, 1), (3, 2), (4, 1), (5, 1) So, they could have the DJ for 3 hours, and the band for 2 hours, among 5 other possibilities

46. PROBLEM SET

47. PROBLEM SET p. 364 #1-21 odd, 23-30 all “Try to learn something about everything and everything about something.” - Thomas H. Huxley

Int Math 2 Section 8-7

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