Grade 9 · Math · Algebra 1

9th grade Systems of inequalities: is this point a solution, and graph the overlap worksheet

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Systems of inequalities: is this point a solution, and graph the overlap

Grade 9 Math Worksheet

NameDate

Circle the best answer.

1.
Jun graphs two inequalities on one grid. Which system does the graph show?
- y ≥ 2x - 2 and y > -x + 5
- y < 2x - 2 and y ≥ -x + 5
- y ≤ 2x - 2 and y > x + 5
- y ≤ 2x - 2 and y > -x + 5
2.
Kira graphs two inequalities on one grid. Which system does the graph show?
- y < 2x + 4 and y ≥ x - 1
- y < -2x + 4 and y ≤ x - 1
- y < -2x + 4 and y ≥ x - 1
- y ≤ -2x + 4 and y > x - 1
3.
Luz graphs two inequalities on one grid. Which system does the graph show?
- y ≥ x + 3 and y < -2x + 7
- y ≤ x + 3 and y < -2x + 7
- y > x + 3 and y ≤ -2x + 7
- y ≥ x + 3 and y < 2x + 7
4.
Luz buys x notebooks at $2 and y pens at $1. Luz spends at most $12 and buys at least 5 items. Which system fits?
- 2x + y ≤ 12 and 2x + y ≥ 5
- 2x + y ≤ 12 and x + y ≤ 5
- x + 2y ≤ 12 and x + y ≥ 5
- 2x + y ≤ 12 and x + y ≥ 5
5.
Pia sells x muffins at $3 and y juices at $2. Pia wants more than $20, and sells fewer than 15 items. Which system fits?
- 2x + 3y > 20 and x + y < 15
- 3x + 2y > 20 and x + y > 15
- 3x + 2y > 20 and x + y < 15
- 3x + 2y > 20 and 3x + 2y < 15
6.
Luz buys x notebooks at $2 and y pens at $1. The limits: spend at most $12, and buy at least 5 items. Can Luz choose 3 notebooks and 4 pens?
- Yes, the plan fits both limits
- No, the plan breaks both limits
- No, the plan breaks the money limit
- No, the plan breaks the item limit
7.
Luz buys x notebooks at $2 and y pens at $1. The limits: spend at most $12, and buy at least 5 items. Can Luz choose 5 notebooks and 3 pens?
- No, the plan breaks the item limit
- No, the plan breaks the money limit
- Yes, the plan fits both limits
- No, the plan breaks both limits
8.
Noah loads x backpacks at 3 kg and y tents at 5 kg. The limits: at most 24 kg, and at least 2 things. Can Noah choose 3 backpacks and 3 tents?
- Yes, the plan fits both limits
- No, the plan breaks the weight limit
- No, the plan breaks the item limit
- No, the plan breaks both limits
9.
Noah loads x backpacks at 3 kg and y tents at 5 kg. The limits: at most 24 kg, and at least 2 things. Can Noah choose 1 backpack and 0 tents?
- No, the plan breaks the weight limit
- No, the plan breaks both limits
- No, the plan breaks the item limit
- Yes, the plan fits both limits
10.
Zee plans x walks at 15 minutes and y bike rides at 10 minutes. The limits: fewer than 60 minutes, and at least 3 trips. Can Zee choose 3 walks and 2 bike rides?
- Yes, the plan fits both limits
- No, the plan breaks the time limit
- No, the plan breaks both limits
- No, the plan breaks the trip limit

9th grade Systems of inequalities: is this point a solution, and graph the overlap worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Systems of inequalities: is this point a solution, and where is the overlap. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can test a point in both inequalities, and I know a point on a dashed line does not count.
I can say where two shaded sides overlap, write the system from the graph, and find the corner where the lines meet.
I can write two limits from a story and check a plan against both.

Standard: A-REI.D.12, A-CED.A.3

Words to know

system of inequalities: Two inequalities about the same x and y.

solution: A point that makes both inequalities true: it is in both shaded sides.

overlap: The part of the graph that both shadings cover.

corner: A point where the two boundary lines meet.

constraint: A limit in a story, written as an inequality.

viable: A plan that fits every limit.

Common mistakes

Your child left out a point on a solid line.

Your child counted a point on a dashed line.

Your child checked a point in only one inequality.

What to say

Ask: does ≤ or ≥ keep the points on the line?

Ask: does < or > include the points on the line?

Ask: does it also pass the other one?

Questions parents ask

What is the most common mistake with systems of inequalities: is this point a solution, and graph the overlap?

Your child left out a point on a solid line.

How can I help my child with systems of inequalities: is this point a solution, and graph the overlap?

Ask: does ≤ or ≥ keep the points on the line?

Are these 9th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More algebra 1

See all Algebra 1

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