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Simultaneous equations: Edexcel GCSE Maths questions

Every Edexcel GCSE Maths exam question on A19 Simultaneous equations, 2017–2025, with its mark scheme and examiner’s report.

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  1. Q21

    June 2025 · Paper 3H

    5 marksA19 Simultaneous equations
    The whole paper ↗
    June 2025 Paper 3H, question 21: Solve algebraically the simultaneous equations 2 + 2y 2 = 44 3x 3x + y = 2

  2. Q10

    November 2024 · Paper 2H

    4 marksA19 Simultaneous equations
    The whole paper ↗
    November 2024 Paper 2H, question 10: Use algebra to solve the simultaneous equations 4x – 5y = 20 6x + 7y = –57 You must show all your working. x = y =

  3. Q20

    November 2024 · Paper 3H

    4 marksA19 Simultaneous equations
    The whole paper ↗
    November 2024 Paper 3H, question 20: Solve the simultaneous equations 2 = 3x 2 + 4 y y + 2x = 7 Give your solutions correct to 3 significant figures.

  4. Q10

    June 2024 · Paper 1H

    4 marksA19 Simultaneous equations
    The whole paper ↗
    June 2024 Paper 1H, question 10: Solve the simultaneous equations 5x – 2y = 23 2x – 3y = 18 x = y =

  5. Q21

    November 2023 · Paper 1H

    5 marksA16 Equation of a circle and tangentsA19 Simultaneous equations
    The whole paper ↗
    November 2023 Paper 1H, question 21: (a) On the grid, draw the graph of x2 + y2 = 169 y 14 12 10 8 6 4 2 O x –14 –12 –10 –8 –6 –4 –2 2 4 6 8 10 12 14 –2 –4 –6 –8 –10 –12 –14 (b) Use your graph to f

  6. Q9

    June 2023 · Paper 1H

    1 markA19 Simultaneous equations
    The whole paper ↗
    June 2023 Paper 1H, question 9:  y 5 2y = 3x – 22 x –5 O 5 10 15 2 – 2y = x –5 –10 –15 Use these graphs to solve the simultaneous equations 2 – 2y = x 2y = 3x – 22 x = y =

  7. Q11

    June 2023 · Paper 2H

    4 marksA19 Simultaneous equations
    The whole paper ↗
    June 2023 Paper 2H, question 11: Use algebra to solve the simultaneous equations 2x + 6y = 5 3x – 4y = –12 x = y =

  8. Q12

    November 2022 · Paper 1H

    4 marksA19 Simultaneous equations
    The whole paper ↗
    November 2022 Paper 1H, question 12: Solve the simultaneous equations 5x + 2y = 11 4x + 3y = 6 x = y =

  9. Q22

    June 2022 · Paper 3H

    5 marksA19 Simultaneous equations
    The whole paper ↗
    June 2022 Paper 3H, question 22: L is the straight line with equation y = 2x − 5 C is a graph with equation y 2 = 6x 2 − 25x − 8 Using algebra, find the coordinates of the points of intersectio

  10. Q20

    November 2021 · Paper 1H

    3 marksA19 Simultaneous equationsA16 Equation of a circle and tangents
    The whole paper ↗
    November 2021 Paper 1H, question 20: The diagram shows the graph of x2 + y2 = 30.25 y 7 6 5 4 3 2 1 O x –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 –1 –2 –3 –4 –5 –6 –7 Use the graph to find estimates for t

  11. Q16

    November 2021 · Paper 3H

    4 marksA19 Simultaneous equationsA18 Quadratic equations
    The whole paper ↗
    November 2021 Paper 3H, question 16: The curve C has equation y = x2 + 3x – 3 The line L has equation y – 5x + 4 = 0 Show, algebraically, that C and L have exactly one point in common.

  12. Q6

    November 2020 · Paper 3H

    3 marksA19 Simultaneous equationsA18 Quadratic equations
    The whole paper ↗
    November 2020 Paper 3H, question 6: y 8 5x − 9y = − 46 6 4 2 O −10 −8 − 6 − 4 −2 2 4 x −2 −4 y = −2x (a) Use these graphs to solve the simultaneous equations 5x − 9y = −46 y = −2x x = y = . y 10 8

  13. Q10

    June 2019 · Paper 1H

    2 marksA19 Simultaneous equations
    The whole paper ↗
    June 2019 Paper 1H, question 10: The graphs with equations 3y + 2x = 1 2 and 2y – 3x = –113 12 have been drawn on the grid below. y 1 3 O x –1 1 2 –1 –2 –3 Using the graphs, find estimates of t

  14. Q20

    June 2019 · Paper 3H

    5 marksA19 Simultaneous equations
    The whole paper ↗
    June 2019 Paper 3H, question 20: Solve algebraically the simultaneous equations x2  4y2 9 3x  4y 7

  15. Q6

    November 2018 · Paper 1H

    3 marksA19 Simultaneous equations
    The whole paper ↗
    November 2018 Paper 1H, question 6: Solve the simultaneous equations 5x + y = 21 xíy = 9 x = y =

  16. Q18

    November 2018 · Paper 2H

    4 marksA9 Straight-line graphsA19 Simultaneous equations
    The whole paper ↗
    November 2018 Paper 2H, question 18: The straight line L1 passes through the points with coordinates (4, 6) and (12, 2) The straight line L2SDVVHVWKURXJKWKHRULJLQDQGKDVJUDGLHQWí The lines

  17. Q19

    November 2018 · Paper 3H

    5 marksA19 Simultaneous equations
    The whole paper ↗
    November 2018 Paper 3H, question 19: Solve algebraically the simultaneous equations 2x2íy2 = 17 x + 2y = 1

  18. Q16

    June 2018 · Paper 2H

    5 marksA19 Simultaneous equationsA16 Equation of a circle and tangents
    The whole paper ↗
    June 2018 Paper 2H, question 16: (a) On the grid, draw the graph of x2 + y2 = 12.25 y 6 4 2 x O –6 –4 –2 2 4 6 –2 –4 –6 (b) Hence find estimates for the solutions of the simultaneous equations

  19. Q11

    November 2017 · Paper 1H

    4 marksA19 Simultaneous equations
    The whole paper ↗
    November 2017 Paper 1H, question 11: 3 teas and 2 coffees have a total cost of £7.80 5 teas and 4 coffees have a total cost of £14.20 Work out the cost of one tea and the cost of one coffee. tea £

  20. Q20

    November 2017 · Paper 1H

    4 marksG21 Exact trigonometric valuesA19 Simultaneous equations
    The whole paper ↗
    November 2017 Paper 1H, question 20: The table shows some values of x and y that satisfy the equation y = acos xq+ b x 0 30 60 90 120 150 180 y 3 1 + 2 1 0 1 – –1 3 3 Find the value of y when x =
All 23 questions on Simultaneous equations, as a list
  1. June 2025, Paper 3H, Q21 (5 marks): Solve algebraically the simultaneous equations 2 + 2y 2 = 44 3x 3x + y = 2
  2. November 2024, Paper 2H, Q10 (4 marks): Use algebra to solve the simultaneous equations 4x – 5y = 20 6x + 7y = –57 You must show all your working. x = y =
  3. November 2024, Paper 3H, Q20 (4 marks): Solve the simultaneous equations 2 = 3x 2 + 4 y y + 2x = 7 Give your solutions correct to 3 significant figures.
  4. June 2024, Paper 1H, Q10 (4 marks): Solve the simultaneous equations 5x – 2y = 23 2x – 3y = 18 x = y =
  5. November 2023, Paper 1H, Q21 (5 marks): (a) On the grid, draw the graph of x2 + y2 = 169 y 14 12 10 8 6 4 2 O x –14 –12 –10 –8 –6 –4 –2 2 4 6 8 10 12 14 –2 –4 –6 –8 –10 –12 –14 (b) Use your graph to f
  6. June 2023, Paper 1H, Q9 (1 mark):  y 5 2y = 3x – 22 x –5 O 5 10 15 2 – 2y = x –5 –10 –15 Use these graphs to solve the simultaneous equations 2 – 2y = x 2y = 3x – 22 x = y =
  7. June 2023, Paper 2H, Q11 (4 marks): Use algebra to solve the simultaneous equations 2x + 6y = 5 3x – 4y = –12 x = y =
  8. November 2022, Paper 1H, Q12 (4 marks): Solve the simultaneous equations 5x + 2y = 11 4x + 3y = 6 x = y =
  9. June 2022, Paper 3H, Q22 (5 marks): L is the straight line with equation y = 2x − 5 C is a graph with equation y 2 = 6x 2 − 25x − 8 Using algebra, find the coordinates of the points of intersectio
  10. November 2021, Paper 1H, Q20 (3 marks): The diagram shows the graph of x2 + y2 = 30.25 y 7 6 5 4 3 2 1 O x –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 –1 –2 –3 –4 –5 –6 –7 Use the graph to find estimates for t
  11. November 2021, Paper 3H, Q16 (4 marks): The curve C has equation y = x2 + 3x – 3 The line L has equation y – 5x + 4 = 0 Show, algebraically, that C and L have exactly one point in common.
  12. November 2020, Paper 3H, Q6 (3 marks): y 8 5x − 9y = − 46 6 4 2 O −10 −8 − 6 − 4 −2 2 4 x −2 −4 y = −2x (a) Use these graphs to solve the simultaneous equations 5x − 9y = −46 y = −2x x = y = . y 10 8
  13. June 2019, Paper 1H, Q10 (2 marks): The graphs with equations 3y + 2x = 1 2 and 2y – 3x = –113 12 have been drawn on the grid below. y 1 3 O x –1 1 2 –1 –2 –3 Using the graphs, find estimates of t
  14. June 2019, Paper 3H, Q20 (5 marks): Solve algebraically the simultaneous equations x2  4y2 9 3x  4y 7
  15. November 2018, Paper 1H, Q6 (3 marks): Solve the simultaneous equations 5x + y = 21 xíy = 9 x = y =
  16. November 2018, Paper 2H, Q18 (4 marks): The straight line L1 passes through the points with coordinates (4, 6) and (12, 2) The straight line L2SDVVHVWKURXJKWKHRULJLQDQGKDVJUDGLHQWí The lines
  17. November 2018, Paper 3H, Q19 (5 marks): Solve algebraically the simultaneous equations 2x2íy2 = 17 x + 2y = 1
  18. June 2018, Paper 2H, Q16 (5 marks): (a) On the grid, draw the graph of x2 + y2 = 12.25 y 6 4 2 x O –6 –4 –2 2 4 6 –2 –4 –6 (b) Hence find estimates for the solutions of the simultaneous equations
  19. November 2017, Paper 1H, Q11 (4 marks): 3 teas and 2 coffees have a total cost of £7.80 5 teas and 4 coffees have a total cost of £14.20 Work out the cost of one tea and the cost of one coffee. tea £
  20. November 2017, Paper 1H, Q20 (4 marks): The table shows some values of x and y that satisfy the equation y = acos xq+ b x 0 30 60 90 120 150 180 y 3 1 + 2 1 0 1 – –1 3 3 Find the value of y when x =
  21. November 2017, Paper 3H, Q19 (5 marks): Prove algebraically that the straight line with equation xíy = 10 is a tangent to the circle with equation x௘2 + y௘2 = 20
  22. June 2017, Paper 1H, Q20 (5 marks): Solve algebraically the simultaneous equations x2 + y2 = 25 y – 3x = 13
  23. June 2017, Paper 3H, Q2 (3 marks): Solve the simultaneous equations 3x + y = –4 3x – 4y = 6 x = y =

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