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?

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

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

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

   y = 2x + 1 and y = -x + 2. Noah tests four points on y < 2x + 1 and y > -x + 2. Which point makes both inequalities true?

   • (2, 1)
   • (1, 0)
   • (0, 3)
   • (1, 1)
5. 5.

   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)
6. 6.

   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?

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

   Tala shades y > x + 1 in red and y < x + 5 in blue. Where do the colors overlap?

   • Everywhere
   • The strip between the two lines
   • Above the lower line
8. 8.

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

   • Above the lower line
   • The strip between the two lines
   • Everywhere
9. 9.

   Ari shades y > 2x + 1 in red and y > 2x + 4 in blue. Where do the colors overlap?

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

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

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