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# Int Math 2 Section 8-7

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Systems of Inequalities

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• ### Int Math 2 Section 8-7

1. 1. SECTION 8-7Systems 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 1Graph the following linear inequalities on separatecoordinates, then again on the same coordinates. y < 2x + 3 y ≥ −3x + 4
4. 4. EXAMPLE 1Graph the following linear inequalities on separatecoordinates, then again on the same coordinates. y < 2x + 3 y ≥ −3x + 4
5. 5. EXAMPLE 1Graph the following linear inequalities on separatecoordinates, then again on the same coordinates. y < 2x + 3 y ≥ −3x + 4
6. 6. EXAMPLE 1Graph the following linear inequalities on separatecoordinates, then again on the same coordinates. y < 2x + 3 y ≥ −3x + 4
7. 7. EXAMPLE 1Graph the following linear inequalities on separatecoordinates, then again on the same coordinates. y < 2x + 3 y ≥ −3x + 4
8. 8. EXAMPLE 1Graph the following linear inequalities on separatecoordinates, then again on the same coordinates. y < 2x + 3 y ≥ −3x + 4
9. 9. EXAMPLE 1Graph the following linear inequalities on separatecoordinates, then again on the same coordinates. y < 2x + 3 y ≥ −3x + 4
10. 10. EXAMPLE 1Graph the following linear inequalities on separatecoordinates, then again on the same coordinates. y < 2x + 3 y ≥ −3x + 4
11. 11. EXAMPLE 1Graph the following linear inequalities on separatecoordinates, then again on the same coordinates. y < 2x + 3 y ≥ −3x + 4
12. 12. EXAMPLE 1Graph the following linear inequalities on separatecoordinates, then again on the same coordinates.
13. 13. EXAMPLE 1Graph the following linear inequalities on separatecoordinates, then again on the same coordinates.
14. 14. EXAMPLE 1Graph the following linear inequalities on separatecoordinates, then again on the same coordinates.
15. 15. EXAMPLE 1Graph the following linear inequalities on separatecoordinates, then again on the same coordinates.
16. 16. EXAMPLE 2Write a system of linear inequalities for the graph shown.
17. 17. EXAMPLE 2Write 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 tohire 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. 19. EXAMPLE 3 Matt Mitarnowski was planning a wedding reception that will last at least 4 hours. The couple wants tohire 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. 20. EXAMPLE 3 Matt Mitarnowski was planning a wedding reception that will last at least 4 hours. The couple wants tohire 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 = bandTime:
21. 21. EXAMPLE 3 Matt Mitarnowski was planning a wedding reception that will last at least 4 hours. The couple wants tohire 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 = bandTime: x + y ≥ 4
22. 22. EXAMPLE 3 Matt Mitarnowski was planning a wedding reception that will last at least 4 hours. The couple wants tohire 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 = bandTime: x + y ≥ 4Money:
23. 23. EXAMPLE 3 Matt Mitarnowski was planning a wedding reception that will last at least 4 hours. The couple wants tohire 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 = bandTime: x + y ≥ 4Money: 150x + 300y <1200
24. 24. EXAMPLE 3 Matt Mitarnowski was planning a wedding reception that will last at least 4 hours. The couple wants tohire 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 ≥ 4Time: x + y ≥ 4  150x + 300y <1200Money: 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 <1200x+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 −xy ≥ −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 −xy ≥ −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 −150xy ≥ −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 −150xy ≥ −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 −150xy ≥ −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 −150xy ≥ −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 −150xy ≥ −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 −150xy ≥ −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 −150xy ≥ −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 −150xy ≥ −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 −150xy ≥ −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 −150xy ≥ −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 −150xy ≥ −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 −150xy ≥ −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 −150xy ≥ −x + 4 300y < −150x +1200 300 300 1 y <− x+4 2
43. 43. EXAMPLE 3b. Solve the system by graphing.
44. 44. EXAMPLE 3 b. Solve the system by graphing.(1, 3), (2, 2), (3, 1),(3, 2), (4, 1), (5, 1)
45. 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. 46. PROBLEM SET
47. 47. PROBLEM SET p. 364 #1-21 odd, 23-30 all“Try to learn something about everything and everything about something.” - Thomas H. Huxley