Systems of Linear Inequalities Applications

Write the linear inequality in standard form for this situation: The CRHS science department can spend no more than $2700 on textbooks this year. The department needs to buy both Biology text books, which cost $57 each, and Chemistry textbooks, which cost $72 each.

• 57x + 72y ≥ 2700

• 57x + 72y > 2700

• 57x + 72y < 2700

• 57x + 72y ≤ 2700

Write the linear inequality in standard form for this situation: In order to raise money to attend upcoming competitions, the Math Pentathalon team is selling apple cider and hot chocolate. They hope to make at least $240 by selling hot chocolate for $1 a glass and hot apple cider for $2 a glass.

• x + 2y < 240

• x + 2y > 240

• x + 2y ≤ 240

• x + 2y ≥ 240

Write the linear inequality in standard form for this situation: Ms. Savva is ordering pizzas and breadsticks for a school party and has a budget of no more than $81. An order of breadsticks costs $7 and a pizza costs $13. 

• 7x + 13y < 81

• 7x + 13y ≥ 81

• 7x + 13y ≤ 81

• 7x + 13y > 81

Beyonce wanted to host a barbecue for Spring Break next week. A package of hot dogs cost $1.60, and a package of hamburgers costs $5. Beyonce bought a total of 8 packages of meat and spent $23 total. Write a system for this situation. Assume "x" represents # of hot dog packages and "y" represent # of hamburger packages.

• x + y = 8
  1.60x + 5y = 23

• x + y = 23
  1.60x + 5y = 8

• x + y = 8
  1.60y + 5x = 23

• x + y = 23
  1.60y + 5x = 8

• (8,4)

• (10,2)

• (7,9)

• (5,9)

• A

• B

• C

• D

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

• (0, 0)

• (-3, 0)

• (2, -5)

• (3, -1)

Which of the following is NOT a solution to the systems of inequalities?

• (0, 0)

• (3, -2)

• (3, -4)

• (4, -4)

Two inequalities are graphed on the same coordinate plane.

Select two solutions to this system of inequalities.

• (6,-2)

• (4,-6)

• (6,-8)

• (-4,0)

Determine whether each ordered pair is a solution or not a solution to this system of inequalities.

y≥−x ​

2x+y>2

• Not a solution

• (5,6)

• Solution

• (4, -5)

• Not a solution

• (0,0)

• Solution

• (2,3)

• Not a solution

• (2,-2)