Systems of Inequalities

Tell whether the ordered pair

(-3, 0) is a solution of the given system.

y ≤ x + 4

y ≥ 2x - 6

• Yes.

• No.

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

Write the system of inequalities Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing

• x + y ≤ 300

  7.5x + 5.5y ≥ 2000

• x + y < 300

  7.5x + 5.5y ≥ 2000

• x + y ≤ 300

  7.5x + 5.5y ≤ 2000

• x + y > 2000

  7.5x + 5.5y ≤ 300

Choose each point that is a solution.

• (0, 6)

• (-3, 4)

• (1, 0)

• (-4, 2)

• (3, 5)

The common shaded area is green. Is (1, -2) a solution?

• Yes.

• No.

The common shaded area is green. Is (3, 1) a solution?

• Yes.

• No.

Does this system of inequalities have a solution?

• Yes.

• No.

The dark green color is the common shaded area. Is (2, 3) a solution to this system of inequalities?

• Yes.

• No.

Kate is selling bracelets and earrings on Etsy to make money for summer vacation. The bracelets (x) cost $2 and earrings (y) cost $3. She needs to make at least $100, but can only make up to 40 pieces of jewelry. Which inequalities represent this situation?

• 2x + 3y > 100

  x + y ≤ 40

• 100x + 2y > 3

  x + y ≤ 40

• 100x + 40y > 100

  3x + 2y ≤ 40

• 3x + 2y > 100

  x + y ≤ 40

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

• (0, 0)

• (-3, 0)

• (2, -5)

• (3, -1)