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 - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

Noah plots points with whole-number x and y from 0 to 6. How many points make both y > x and x + y ≤ 6 true?
Pia plots points with whole-number x and y from 0 to 6. How many points make both y ≥ 2x and x + y < 7 true?
Ren plots points with whole-number x and y from 0 to 5. How many points make both y < x + 3 and 2x + y ≥ 5 true?
Tala plots points with whole-number x and y from 0 to 5. How many points make both x + y > 4 and x + y ≤ 7 true?
5.
Zee shades y > 2x - 1 and y < -x + 8. The two boundary lines meet at a corner of the overlap. Which point is the corner?
- (5, 3)
- (4, 7)
- (3, 5)
- (0, -1)
6.
Ari shades y > x + 2 and y < -2x + 8. The two boundary lines meet at a corner of the overlap. Which point is the corner?
- (0, 2)
- (2, 4)
- (3, 5)
- (4, 2)
7.
Bo shades y > 3x - 4 and y < -x + 12. The two boundary lines meet at a corner of the overlap. Which point is the corner?
- (4, 8)
- (0, -4)
- (5, 11)
- (8, 4)
8.
Esme shades y > -x + 7 and y < 2x - 2. The two boundary lines meet at a corner of the overlap. Which point is the corner?
- (4, 3)
- (2, 5)
- (3, 4)
- (0, 7)
9.
Jun graphs y > x + 2 and y < x + 7. Where is the overlap of the two shaded sides?
- A strip between the two lines
- No point makes both true
- Everything above both lines
- Only the points on the line
10.
Kira graphs y ≥ 2x - 3 and y ≤ 2x + 1. Where is the overlap of the two shaded sides?
- A strip between the two lines
- No point makes both true
- Only the points on the line
- Everything above both lines

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

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