Ordered Pair Must Be a Solution of All Inequalities

Which ordered pair is in the solution set of the following system of inequalities?

y < 1/2x + 4

y ≥ –x + 1

• (-5, 3)

• (0, 4)

• (3, -5)

• (4, 0)

Which ordered pair is in the solution set of the following system of linear inequalities?

y < 2x + 2

y ≥ −x − 1

• (0, 3)

• (2, 0)

• (-1, 0)

• (-1, -4)

Which ordered pair is in the solution set of the system of linear inequalities graphed below?

• (1, -4)

• (-5, 7)

• (5, 3)

• (-7, -2)

A group of friends will buy at most 8 snacks at a movie theater and spend no more than $42. They will pay $4 for each box of candy and $7 for each bag of popcorn. The system of inequalities graphed below represents this information.

• 2 boxes of candy and 6 bags of popcorn

• 3 boxes of candy and 4 bags of popcorn

• 5 boxes of candy and 4 bags of popcorn

• 8 boxes of candy and 1 bags of popcorn

A band is determining how many songs to record for a new album. The band members want to record no more than 16 songs, and their album has to be shorter than 78 minutes. They can record short songs that are about 3 minutes in length or long songs that are about 5 minutes in length. Which system of inequalities best represents the number of short songs (x) and the number of long songs (y) the band can record for the new album?

• x + y < 16

  3x + 5y ≤ 78

• x + y ≤ 16

  3x + 5y < 78

• x + y ≤ 78

  3x + 5y < 16

• x + y < 78

  3x + 5y ≤ 16

Eddie mows lawns and paints houses to earn extra money. He never spends more than 15 hours a week mowing lawns and painting houses. He always spends at least as much time painting houses as he does mowing lawns. Which graph shows all the possible combinations of hours Eddie could spend mowing lawns and painting houses in a week?

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Amy repairs cars and trucks. Last year, she repaired more cars than trucks. She also repaired at least 14 cars and trucks in all. To represent this situation, Amy wrote the system of inequalities shown below.

x > y

x + y ≥ 14

What does the solution (9, 7) represent in Amy’s system?

• Amy repaired 9 cars and 7 trucks last year.

• Amy repaired 9 trucks and 7 cars last year.

• Amy repaired 9 vehicles last year, 7 of which were cars.

• Amy repaired 9 vehicles last year, 7 of which were trucks.

Natalie makes flower arrangements using tulips and lilies. She wants each arrangement to have no more than 12 flowers. She also wants each arrangment to have at least twice as many tulips as lilies. To represent the possible numbers of tulips and lilies in a flower arrangement, Natalie wrote the system of inequalities shown below.

x + y ≤ 12

x ≥ 2y

The point (8, 3) is a solution to the system of inequalities. What is represented by the solution (8, 3)?

• Natalie could make a flower arrangement with 8 lilies and 3 tulips.

• Natalie could make a flower arrangement with 8 tulips and 3 lilies.

• Natalie could make a flower arrangement with 8 flowers in total, 3 of which are lilies.

• Natalie could make a flower arrangement with 8 flowers in total, 3 of which are tulips.

Victoria is a chemist. As part of an experiment, she mixes an acid with water. She wants the volume of the mixture to measure at least 8 deciliters. She also wants the mixture to be at least 2/3 water. To represent this situation, Victoria draws the lines for a system of inequalities as shown below.

• Region A

• Region B

• Region C

• Region D

Craig earns at least $100 each week. He works no more than 18 hours each week. He earns $5 per hour mowing lawns and $7 per hour tutoring. Which graph shows all the possible hours Craig can work mowing lawns and tutoring in a week?

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