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Integrated Math 2 Section 8-7
 

Integrated Math 2 Section 8-7

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Systems of Inequalities

Systems of Inequalities

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Integrated Math 2 Section 8-7 Integrated Math 2 Section 8-7 Presentation Transcript

  • 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 solution set of a system of linear inequalities? • Where you’ll see this: • Sports, entertainment, retail, finance
  • EXAMPLE 1 Graph the following linear inequalities on separate coordinates, then again on the same coordinates. y < 2x + 3 y ≥ −3x + 4
  • EXAMPLE 1 Graph the following linear inequalities on separate coordinates, then again on the same coordinates. y < 2x + 3 y ≥ −3x + 4
  • EXAMPLE 1 Graph the following linear inequalities on separate coordinates, then again on the same coordinates. y < 2x + 3 y ≥ −3x + 4
  • EXAMPLE 1 Graph the following linear inequalities on separate coordinates, then again on the same coordinates. y < 2x + 3 y ≥ −3x + 4
  • EXAMPLE 1 Graph the following linear inequalities on separate coordinates, then again on the same coordinates. y < 2x + 3 y ≥ −3x + 4
  • EXAMPLE 1 Graph the following linear inequalities on separate coordinates, then again on the same coordinates. y < 2x + 3 y ≥ −3x + 4
  • EXAMPLE 1 Graph the following linear inequalities on separate coordinates, then again on the same coordinates. y < 2x + 3 y ≥ −3x + 4
  • EXAMPLE 1 Graph the following linear inequalities on separate coordinates, then again on the same coordinates. y < 2x + 3 y ≥ −3x + 4
  • EXAMPLE 1 Graph the following linear inequalities on separate coordinates, then again on the same coordinates. y < 2x + 3 y ≥ −3x + 4
  • 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 ≥ −4x + 6   1 y < x − 3  2
  • 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.
  • 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
  • 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:
  • 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
  • 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:
  • 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
  • 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
  • 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 −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 −x −x −150x −150x y ≥ −x + 4
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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 about something.” - Thomas H. Huxley