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.

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

   • y ≥ 3x - 3 and y < -2x + 8
   • y > 3x - 3 and y ≤ 2x + 8
   • y > 3x - 3 and y ≤ -2x + 8
   • y > 3x - 3 and y ≥ -2x + 8
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 2x + y ≥ 5
   • x + 2y ≤ 12 and x + y ≥ 5
   • 2x + y ≤ 12 and x + y ≤ 5
   • 2x + y ≤ 12 and x + y ≥ 5
6. 6.

   Noah packs x backpacks at 3 kg and y tents at 5 kg. The load is at most 24 kg, and Noah packs at least 2 things. Which system fits?

   • 3x + 5y ≤ 24 and x + y ≤ 2
   • 5x + 3y ≤ 24 and x + y ≥ 2
   • 3x + 5y ≤ 24 and 3x + 5y ≥ 2
   • 3x + 5y ≤ 24 and x + y ≥ 2
7. 7.

   Zee has fewer than 60 minutes. A walk takes 15 minutes (x) and a bike ride 10 minutes (y). Zee wants at least 3 trips. Which system fits?

   • 15x + 10y < 60 and x + y ≤ 3
   • 10x + 15y < 60 and x + y ≥ 3
   • 15x + 10y < 60 and x + y ≥ 3
   • 15x + 10y < 60 and 15x + 10y ≥ 3
8. 8.

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

   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 3 backpacks and 3 tents?

   • No, the plan breaks the weight limit
   • No, the plan breaks the item limit
   • No, the plan breaks both limits
   • Yes, the plan fits both limits
10. 10.

    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?

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