Systems with a quadratic: a line and a parabola, a line and a circle, two parabolas

Grade 11 Math Worksheet

Circle the best answer.

1. 1.

   Pia solves the system y = x² − 3 and y = 2x. Which lists every solution?

   • (-1, -2) and (3, 6)
   • (-1, 0) and (3, 0)
   • (3, 6)
   • (1, -2) and (-3, 6)
2. 2.

   Ren solves the system y = x² + 2x − 1 and y = x + 1. Which lists every solution?

   • (-2, -1) and (1, 2)
   • (1, 2)
   • (2, -1) and (-1, 2)
   • (-2, 0) and (1, 0)
3. 3.

   Esme solves the system y = x² − 4x + 1 and y = -2x + 4. Which lists every solution?

   • (1, 6) and (-3, -2)
   • (3, -2)
   • (-1, 6) and (3, -2)
   • (-1, 0) and (3, 0)
4. 4.

   Jun solves the system x² + y² = 25 and y = x + 1. Which lists every solution?

   • (-3, -4) and (4, 3)
   • (-4, -3) and (3, 4)
   • (-4, 3) and (3, 4)
   • (3, 4)
5. 5.

   Luz solves the system x² + y² = 25 and y = x − 1. Which lists every solution?

   • (-3, 4) and (4, 3)
   • (4, 3)
   • (-4, -3) and (3, 4)
   • (-3, -4) and (4, 3)
6. 6.

   Milo solves the system x² + y² = 10 and y = 2x − 5. Which lists every solution?

   • (1, -3) and (3, 1)
   • (1, 3) and (3, 1)
   • (-3, 1) and (1, 3)
   • (3, 1)
7. 7.

   Noah solves the system x² + y² = 13 and y = x + 1. Which lists every solution?

   • (-3, 2) and (2, 3)
   • (2, 3)
   • (-2, -3) and (3, 2)
   • (-3, -2) and (2, 3)
8. 8.

   Pia solves the system y = x² + 2x − 1 and y = -x² + 4x + 3 by subtracting. Which lists every solution?

   • (2, 7)
   • (-1, -2) and (2, 7)
   • (-1, 0) and (2, 0)
   • (-1, 2) and (2, -7)
9. 9.

   Zee solves the system y = 2x² − 3x and y = x² + x − 3 by subtracting. Which lists every solution?

   • (1, 1) and (3, -9)
   • (3, 9)
   • (1, -1) and (3, 9)
   • (1, 0) and (3, 0)
10. 10.

    Esme solves the system y = x² + x and y = -x² − x + 4 by subtracting. Which lists every solution?

    • (-2, 0) and (1, 0)
    • (-2, -2) and (1, -2)
    • (-2, 2) and (1, 2)
    • (1, 2)