Systems of Inequalities

Which of the following inequalities matches the given graph?

• y ≤ -3/4 x + 3

• y ≥ -3/4 x + 3

• y < -3/4 x + 3

• y > -3/4 x + 3

Which of the following is not a solution to this system of inequalities?

• (0,-1)

• (0,3)

• (4,0)

• (6,-2)

Which system of inequalities matches the graph?

• y > 2x - 4
  y < 2

• y < 2x - 4
  y < 2

• y > 2x - 4
  y <  2 

• y < 2x - 4
  y <   -2

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

• (1,3)

• (2,1)

• (3,4)

• (6,2)

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

Is (-2,4) a solution to the system?

• Solution

• Not a solution

This graph matches which inequality?

• y > 3

• y ≥ 3

• x≥3

• x>3

Given the system, determine a solution.

• No solution

• Infinite solutions

• (-5, 5)

• (5, -5)

Which system of linear inequalities is represented by the graph?

• y≤2x-1
  y>-2x+3

• y>2x-1
  y≤-2x+3

• y<2x-1
  y≥-2x+3

• y≤2x-1
  y>2x+3