System of Inequalities Graph and Word Problems

Write the system of inequalities
Eiko is drawing caricatures at a fair for 8 hours (480 minutes). She can complete a small drawing in 15 minutes and charges $10 for the drawing. She can complete a larger drawing in 45 minutes and charges $25 for the drawing. Eiko hopes to make at least $200 at the fair. 

• 10x+15y≤480
  45x+25y≥250

• 10x+25y≤200
  15x+45y≤480

• 10x+25y>200
  15x+45y<480

• 10x+25y≥200
  15x+45y≤480

Cullin needs to save at least $100 for homecoming. He works 2 jobs earning $8/hour at Culvers and $25/hour mowing lawns. He only has time to work 14 hours before homecoming.

• x + y  ≥ 25
  x + y ≤ 8

• 100x + 25 y ≤ 100
  2x + 8y ≤ 14

• x + y ≥ 100
  8x + 25y ≤ 14

• 8x + 25y ≥ 100
  x + y ≤ 14

Cole is doing a basketball challenge for charity. In order to win money for the charity, he needs to score at least 20 points in less than 10 shots. If x is the number of 2-point shots, and y is the number of three point shots, which inequalities below represent the situation?

• x + y < 10

  2x + 3y ≥ 20

• x + y ≤ 10

  2x + 3y ≥ 20

• x + y ≤ 10

  2x + 3y > 20

• x + y < 10

  2x + 3y > 20

Which point below is NOT part of the solution set?

• (0, 0)

• (5, 1)

• (-1, -3)

• (20, -5)

Which system of inequalities is represented by this graph?

• y < -3x + 3 and y > -3x - 1

• y ≥ -3x + 3 and y ≤ -3x - 1

• y ≤ -3x + 3 and y ≥ -3x - 1

• y > -3x + 3 and y < -3x - 1

Which graph shows the system of linear inequalities?

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Which system of inequalities is represented by the graph?

• x≤-2
  y≤x-3

• y≤-2
  y≤x-3

• x≥-2
  y≤x-3

• y≥-2
  y≤x-3

Solve the system of inequalities by graphing.

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Which system of inequalities is shown?

• y ≥ -x - 1
  y < x + 4

• y < -x - 1
   y ≥ x + 4

• y > -x - 1
  y ≥ x + 4

• y > -x - 1
  y ≥ x + 3

Which system of inequalities matches this graph?

• y≥-2x+3
  y≤x-3

• y>2x+3
  y≥x-3

• y>-2x+3
  y≥x-3

• y<-2x+3
  y≤x-3