Area with Systems of Inequalities

Which area (white, red, purple, blue) do you think represents the solution to this system of inequalities? Explain your reasoning. Remember that a solution makes BOTH inequalities true at the same time.

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Which of the following is a solution to the systems of inequalities?

• (-1, -3)

• (3, 0)

• (-2, 2)

• (4, 1)

Where do you think the solution will be?

• Blue

• Purple

• Red

• White

• All of blue and all of red

What is the solution to the system of linear inequalities: 3x - 2y < 6 and 2x + y > 4?

• The solution is a single point on the graph.

• The solution is the region where the two shaded areas do not overlap.

• The solution is a line on the graph.

• The solution is the region where the two shaded areas overlap.

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 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

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

Lisa gives child(x) and adult(y) haircuts in her salon. She charges $10 for a child and $40 for an adult haircut. Her goal is to make at least $1000 per week and work no more than 40 hours. The shaded region of the graph represents the possible combinations of adult and child haircuts that will allow her to meet her goal. Which combination represents her maximum profit?

• 10 adult haircuts and 60 child haircuts

• 20 adult haircuts and 40 child haircuts

• no adult haircuts and 80 child haircuts

• 40 adult haircuts and no child haircuts

• (1,3)

• (2,1)

• (3,4)

• (6,2)