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

Grade 9 Math Worksheet - Building Confidence

Circle the best answer.

1. 1.

   At x = 3, the rule y = -x + 8 gives 5. Ari already checked that (3, 5) works in y > x + 1. Does (3, 5) also work in y ≤ -x + 8?

   • No, it is on the second line, so it does not count
   • Yes, it is in both shaded sides
   • No, it is on the wrong side of the second line
2. 2.

   At x = 2, the rule y = -x + 5 gives 3. Esme already checked that (2, 6) works in y > x + 1. Does (2, 6) also work in y ≤ -x + 5?

   • No, it is on the wrong side of the second line
   • No, it is on the second line, so it does not count
   • Yes, it is in both shaded sides
3. 3.

   At x = 5, the rule y = -x + 7 gives 2. Jun already checked that (5, 1) works in y < x - 2. Does (5, 1) also work in y > -x + 7?

   • No, it is on the wrong side of the second line
   • No, it is on the second line, so it does not count
   • Yes, it is in both shaded sides
4. 4.

   At x = 1, the rule y = -x + 5 gives 4. Kira already checked that (1, 4) works in y ≥ 2x + 1. Does (1, 4) also work in y ≥ -x + 5?

   • Yes, it is in both shaded sides
   • No, it is on the second line, so it does not count
   • No, it is on the wrong side of the second line
5. 5.

   At x = 2, the rule y = -2x + 7 gives 3. Luz already checked that (2, 3) works in y > x. Does (2, 3) also work in y < -2x + 7?

   • No, it is on the wrong side of the second line
   • Yes, it is in both shaded sides
   • No, it is on the second line, so it does not count
6. 6.

   y = x + 1 and y = -x + 8. Milo tests four points on y > x + 1 and y ≤ -x + 8. Which point makes both inequalities true?

   • (0, 9)
   • (1, 3)
   • (3, 1)
   • (1, 0)
7. 7.

   y = x - 2 and y = -x + 6. Pia tests four points on y ≥ x - 2 and y < -x + 6. Which point makes both inequalities true?

   • (0, 6)
   • (1, 4)
   • (0, 7)
   • (4, 1)
8. 8.

   y = 2x - 3 and y = x + 2. Ren tests four points on y ≥ 2x - 3 and y ≤ x + 2. Which point makes both inequalities true?

   • (2, 0)
   • (0, 3)
   • (3, 2)
   • (2, 3)
9. 9.

   Zee shades y > -2x + 2 in red and y < -2x + 6 in blue. Where do the colors overlap?

   • Everywhere
   • Above the lower line
   • The strip between the two lines
10. 10.

    Bo shades y < -x + 7 in red and y < -x + 3 in blue. Where do the colors overlap?

    • The strip between the two lines
    • Below the lower line
    • Below the higher line