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

Grade 9 Math Worksheet

Circle the best answer.

1. 1.

   Esme graphs two inequalities on one grid. Which system does the graph show?

   • y > 2x + 1 and y ≤ -2x + 6
   • y > 2x + 1 and y ≤ 2x + 6
   • y ≥ 2x + 1 and y < -2x + 6
   • y > 2x + 1 and y ≥ -2x + 6
2. 2.

   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
3. 3.

   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
4. 4.

   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
5. 5.

   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 x + y ≤ 5
   • 2x + y ≤ 12 and x + y ≥ 5
   • x + 2y ≤ 12 and x + y ≥ 5
   • 2x + y ≤ 12 and 2x + y ≥ 5
6. 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 the money limit
   • No, the plan breaks both limits
   • No, the plan breaks the item limit
7. 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 both limits
   • Yes, the plan fits both limits
   • No, the plan breaks the money limit
   • No, the plan breaks the item limit
8. 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 1 backpack and 0 tents?

   • No, the plan breaks both limits
   • Yes, the plan fits both limits
   • No, the plan breaks the weight limit
   • No, the plan breaks the item limit
9. 9.

   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?

   • No, the plan breaks the trip limit
   • Yes, the plan fits both limits
   • No, the plan breaks both limits
   • No, the plan breaks the time limit
10. 10.

    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 4 notebooks and 4 pens?

    • No, the plan breaks both limits
    • Yes, the plan fits both limits
    • No, the plan breaks the item limit
    • No, the plan breaks the money limit