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SECTION 8-7
Systems of Inequalities
ESSENTIAL QUESTIONS

• How do you write a system of linear inequalities for a given
 graph?

• How do you graph the soluti...
EXAMPLE 1
Graph the following linear inequalities on separate
coordinates, then again on the same coordinates.

     y < 2...
EXAMPLE 1
Graph the following linear inequalities on separate
coordinates, then again on the same coordinates.

     y < 2...
EXAMPLE 1
Graph the following linear inequalities on separate
coordinates, then again on the same coordinates.

     y < 2...
EXAMPLE 1
Graph the following linear inequalities on separate
coordinates, then again on the same coordinates.

     y < 2...
EXAMPLE 1
Graph the following linear inequalities on separate
coordinates, then again on the same coordinates.

     y < 2...
EXAMPLE 1
Graph the following linear inequalities on separate
coordinates, then again on the same coordinates.

     y < 2...
EXAMPLE 1
Graph the following linear inequalities on separate
coordinates, then again on the same coordinates.

     y < 2...
EXAMPLE 1
Graph the following linear inequalities on separate
coordinates, then again on the same coordinates.

     y < 2...
EXAMPLE 1
Graph the following linear inequalities on separate
coordinates, then again on the same coordinates.

     y < 2...
EXAMPLE 1
Graph the following linear inequalities on separate
coordinates, then again on the same coordinates.
EXAMPLE 1
Graph the following linear inequalities on separate
coordinates, then again on the same coordinates.
EXAMPLE 1
Graph the following linear inequalities on separate
coordinates, then again on the same coordinates.
EXAMPLE 1
Graph the following linear inequalities on separate
coordinates, then again on the same coordinates.
EXAMPLE 2
Write a system of linear inequalities for the graph shown.
EXAMPLE 2
Write a system of linear inequalities for the graph shown.




                                             y ≥...
EXAMPLE 3
 Matt Mitarnowski was planning a wedding reception
   that will last at least 4 hours. The couple wants to
hire ...
EXAMPLE 3
 Matt Mitarnowski was planning a wedding reception
   that will last at least 4 hours. The couple wants to
hire ...
EXAMPLE 3
 Matt Mitarnowski was planning a wedding reception
   that will last at least 4 hours. The couple wants to
hire ...
EXAMPLE 3
 Matt Mitarnowski was planning a wedding reception
   that will last at least 4 hours. The couple wants to
hire ...
EXAMPLE 3
 Matt Mitarnowski was planning a wedding reception
   that will last at least 4 hours. The couple wants to
hire ...
EXAMPLE 3
 Matt Mitarnowski was planning a wedding reception
   that will last at least 4 hours. The couple wants to
hire ...
EXAMPLE 3
 Matt Mitarnowski was planning a wedding reception
   that will last at least 4 hours. The couple wants to
hire ...
EXAMPLE 3
           b. Solve the system by graphing.
x + y ≥ 4

150x + 300y <1200
EXAMPLE 3
           b. Solve the system by graphing.
x + y ≥ 4

150x + 300y <1200
x+y≥4
EXAMPLE 3
           b. Solve the system by graphing.
x + y ≥ 4

150x + 300y <1200
 x+y≥4
−x  −x
EXAMPLE 3
             b. Solve the system by graphing.
 x + y ≥ 4
 
 150x + 300y <1200
  x+y≥4
−x      −x
y ≥ −x + 4
EXAMPLE 3
             b. Solve the system by graphing.
 x + y ≥ 4
 
 150x + 300y <1200
  x+y≥4      150x + 300y <1200
...
EXAMPLE 3
            b. Solve the system by graphing.
 x + y ≥ 4
 
 150x + 300y <1200
  x + y ≥ 4 150x + 300y <1200
−x...
EXAMPLE 3
            b. Solve the system by graphing.
 x + y ≥ 4
 
 150x + 300y <1200
  x + y ≥ 4 150x + 300y <1200
−x...
EXAMPLE 3
            b. Solve the system by graphing.
 x + y ≥ 4
 
 150x + 300y <1200
  x + y ≥ 4 150x + 300y <1200
−x...
EXAMPLE 3
            b. Solve the system by graphing.
 x + y ≥ 4
 
 150x + 300y <1200
  x + y ≥ 4 150x + 300y <1200
−x...
EXAMPLE 3
            b. Solve the system by graphing.
 x + y ≥ 4
 
 150x + 300y <1200
  x + y ≥ 4 150x + 300y <1200
−x...
EXAMPLE 3
            b. Solve the system by graphing.
 x + y ≥ 4
 
 150x + 300y <1200
  x + y ≥ 4 150x + 300y <1200
−x...
EXAMPLE 3
            b. Solve the system by graphing.
 x + y ≥ 4
 
 150x + 300y <1200
  x + y ≥ 4 150x + 300y <1200
−x...
EXAMPLE 3
            b. Solve the system by graphing.
 x + y ≥ 4
 
 150x + 300y <1200
  x + y ≥ 4 150x + 300y <1200
−x...
EXAMPLE 3
            b. Solve the system by graphing.
 x + y ≥ 4
 
 150x + 300y <1200
  x + y ≥ 4 150x + 300y <1200
−x...
EXAMPLE 3
            b. Solve the system by graphing.
 x + y ≥ 4
 
 150x + 300y <1200
  x + y ≥ 4 150x + 300y <1200
−x...
EXAMPLE 3
            b. Solve the system by graphing.
 x + y ≥ 4
 
 150x + 300y <1200
  x + y ≥ 4 150x + 300y <1200
−x...
EXAMPLE 3
            b. Solve the system by graphing.
 x + y ≥ 4
 
 150x + 300y <1200
  x + y ≥ 4 150x + 300y <1200
−x...
EXAMPLE 3
            b. Solve the system by graphing.
 x + y ≥ 4
 
 150x + 300y <1200
  x + y ≥ 4 150x + 300y <1200
−x...
EXAMPLE 3
b. Solve the system by graphing.
EXAMPLE 3
        b. Solve the system by graphing.




(1, 3), (2, 2), (2, 3),
(3, 1), (4, 1), (5, 1)
HOMEWORK
HOMEWORK


              p. 364 #1-21 odd, 23-30 all




“Try to learn something about everything and everything
         ...
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Systems of Inequalities

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  • Transcript of "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
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