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

Answer Key - Grade 9 Math Worksheet - Challenge Me

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

1. 1.

   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?

   12
2. 2.

   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?

   12
3. 3.

   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?

   23
4. 4.

   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?

   15
5. 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?

   • (3, 5)
   • (4, 7)
   • (5, 3)
   • (0, -1)
6. 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?

   • (3, 5)
   • (4, 2)
   • (2, 4)
   • (0, 2)
7. 7.

   Kira graphs y ≥ 2x - 3 and y ≤ 2x + 1. Where is the overlap of the two shaded sides?

   • Everything above both lines
   • No point makes both true
   • A strip between the two lines
   • Only the points on the line
8. 8.

   Milo graphs y > -x + 6 and y < -x + 2. Where is the overlap of the two shaded sides?

   • Only the points on the line
   • A strip between the two lines
   • No point makes both true
   • Everything above both lines
9. 9.

   Noah graphs y ≥ 2x + 3 and y ≤ 2x + 3. Where is the overlap of the two shaded sides?

   • Only the points on the line
   • Everything above both lines
   • No point makes both true
   • A strip between the two lines
10. 10.

    Pia graphs y ≥ -x + 9 and y ≤ -x + 9. Where is the overlap of the two shaded sides?

    • Everything above both lines
    • A strip between the two lines
    • No point makes both true
    • Only the points on the line