Systems of Linear Inequalities

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

• (0,-1)

• (0,3)

• (4,0)

• (6,-2)

Which are vertices of the feasible region?

• (0, 3) (3, 0) (5, 8)

• (0, 6) (3, 5) (6, 5)

• (3, 3) (8, 5) (5, 8)

• (0, 5) (6, 0) (3, 3)

Solve the system of inequalities. The feasible region is shown by the darkest blue shading.

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Solve each of the following systems of linear inequalities a graphing approach. Verify using a graphing calculator. Which of following are the vertices of the feasible region?

• (2, 0), (4, 5), (6, 0)

• (2, 0), (3, 5), (0, 6)

• (0, 2), (3.5, 4.5), (6, 2)

• (0, 0), (3, 5), (6, 0)

Solve each of the following systems of linear inequalities a graphing approach. Verify using a graphing calculator. Which of following are the corner points?

• (2, 0), (4, 5), (6, 0)

• (2, 0), (3, 5), (0, 6)

• (0, 2), (3.5, 4.5), (6, 2)

• (0, 0), (3, 5), (6, 0)

John has $40 to spend on gifts for his friend. If candy costs $5 each and flowers cost $10 each. Which of the following includes ALL of the vertices of the feasible region for this scenario, if the quantity of candy is represented by the variable x and flowers are represented by y?

• (0,0), (0,10), (8,0)

• (0,0), (10,0),(0.8)

• (10,0),(0,8)

• (0,10).(8,0)

Which point is a solution to the system of inequalities?

• (-8,2)

• (-2,-5)

• (0,6)

• (4, 3)

Answer explanation

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

How many solutions will this system have?

• No solution

• One Solution

• I Don't Know

• Infinitely Many Solutions

Answer explanation

Which of the following points is a solution to the system of equations below? x + 2y ≥ 4 3x − 2y < 4 Take your time! Use the DesMos.com website.

• (0, 0)

• (2, 1)

• (2, 2)

• (-1, 1)