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Linear and quadratic systems

10th grade (Year 11 in England) · 16 questions · Common Core: HSA.REI.C.7 · England: GCSE Higher Algebra

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Date

Score/ 16

  1. Question 1

    Solve the system y = x² − 9x + 20 and y = 2. Give the x-values, separated by a comma.

    xy−8−448−20−16−12−8−4481216200y = 2

    x =

  2. Question 2

    Solve the system y = x² + 3x − 17 and y = 2x − 5. Give the x-values, separated by a comma.

    xy−8−448−20−16−12−8−4481216200y = 2x − 5

    x =

  3. Question 3

    Solve the system y = x² + 3x − 8 and y = −4. Give the x-values, separated by a comma.

    xy−8−448−20−16−12−8−4481216200y = −4

    x =

  4. Question 4

    Solve the system y = x² + 7x + 6 and y = 3x + 3. Give the x-values, separated by a comma.

    xy−8−448−20−16−12−8−4481216200y = 3x + 3

    x =

  5. Question 5

    Solve the system y = x² − 4x − 1 and y = x + 5. Give the x-values, separated by a comma.

    xy−8−448−20−16−12−8−4481216200y = x + 5

    x =

  6. Question 6

    Solve the system y = x² − 11x + 27 and y = −3. Give the x-values, separated by a comma.

    xy−8−448−20−16−12−8−4481216200y = −3

    x =

  7. Question 7

    Solve the system y = x² − 4x − 15 and y = −3x − 3. Give the x-values, separated by a comma.

    xy−8−448−20−16−12−8−4481216200y = −3x − 3

    x =

  8. Question 8

    Solve the system y = x² − x and y = 2. Give the x-values, separated by a comma.

    xy−8−448−20−16−12−8−4481216200y = 2

    x =

  9. Question 9

    Solve the system y = x² + 8x + 8 and y = 2x + 3. Give the x-values, separated by a comma.

    xy−8−448−20−16−12−8−4481216200y = 2x + 3

    x =

  10. Question 10

    Solve the system y = x² + x − 35 and y = 2x − 5. Give the x-values, separated by a comma.

    xy−8−448−20−16−12−8−4481216200y = 2x − 5

    x =

  11. Question 11

    Solve the system y = x² − 7x + 16 and y = 4. Give the x-values, separated by a comma.

    xy−8−448−20−16−12−8−4481216200y = 4

    x =

  12. Question 12

    Solve the system y = x² − 11x + 18 and y = −2x. Give the x-values, separated by a comma.

    xy−8−448−20−16−12−8−4481216200y = −2x

    x =

  13. Question 13

    Solve the system y = x² + 3x − 10 and y = 0. Give the x-values, separated by a comma.

    xy−8−448−20−16−12−8−4481216200y = 0

    x =

  14. Question 14

    Solve the system y = x² + 3x − 14 and y = −4. Give the x-values, separated by a comma.

    xy−8−448−20−16−12−8−4481216200y = −4

    x =

  15. Question 15

    Solve the system y = x² − 2x − 16 and y = −3x − 4. Give the x-values, separated by a comma.

    xy−8−448−20−16−12−8−4481216200y = −3x − 4

    x =

  16. Question 16

    Solve the system y = x² + 5x + 5 and y = −2x − 5. Give the x-values, separated by a comma.

    xy−8−448−20−16−12−8−4481216200y = −2x − 5

    x =

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Answer key: Linear and quadratic systems

  1. 1. x = 3 or x = 6

  2. 2. x = -4 or x = 3

  3. 3. x = -4 or x = 1

  4. 4. x = -3 or x = -1

  5. 5. x = -1 or x = 6

  6. 6. x = 5 or x = 6

  7. 7. x = -3 or x = 4

  8. 8. x = -1 or x = 2

  9. 9. x = -5 or x = -1

  10. 10. x = -5 or x = 6

  11. 11. x = 3 or x = 4

  12. 12. x = 3 or x = 6

  13. 13. x = -5 or x = 2

  14. 14. x = -5 or x = 2

  15. 15. x = -4 or x = 3

  16. 16. x = -5 or x = -2