Int Math 2 Section 8-7

517 views
465 views

Published on

Systems of Inequalities

Published in: Education
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
517
On SlideShare
0
From Embeds
0
Number of Embeds
111
Actions
Shares
0
Downloads
9
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • 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

    ×