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Simultaneous equations: AQA GCSE Maths questions

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

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1,304 questions

  1. Q1

    June 2025 · Paper 1H

    3 marksA19 Simultaneous equations
    The whole paper ↗
    June 2025 Paper 1H, question 1: Solve the simultaneous equations 2x + 5y = 18 2x + y = 6 x = y =

  2. Q24

    November 2024 · Paper 3H

    5 marksA19 Simultaneous equations
    The whole paper ↗
    November 2024 Paper 3H, question 24: A curve has the equation y = x2 + 4x – 4 A straight line has the equation y = 3x – 2 Work out the two points of intersection of the curve and the straight line.

  3. Q14

    June 2024 · Paper 1H

    4 marksA19 Simultaneous equations
    The whole paper ↗
    June 2024 Paper 1H, question 14: 4 chocolate bars and 3 packets of mints cost £4.70 5 chocolate bars and 1 packet of mints cost £4.50 Work out the cost of a chocolate bar and the cost of a pack

  4. Q11

    November 2023 · Paper 3H

    3 marksA19 Simultaneous equations
    The whole paper ↗
    November 2023 Paper 3H, question 11: Solve these simultaneous equations. 7x + 2y = 100 3x + 2y = 48 x = y =

  5. Q16

    June 2023 · Paper 1H

    4 marksA19 Simultaneous equations
    The whole paper ↗
    June 2023 Paper 1H, question 16: Solve the simultaneous equations 2x – 5y = 13 3x + 4y = 8 x = y =

  6. Q16

    November 2022 · Paper 1H

    4 marksA19 Simultaneous equationsA11 Quadratic graphs and turning points
    The whole paper ↗
    November 2022 Paper 1H, question 16: A graph has the equation y = x2 + px + r where p and r are constants. The graph passes through the points (0, 4), (1, 3) and (8, w) Work out the value of w. w =

  7. Q23

    June 2022 · Paper 3H

    3 marksA19 Simultaneous equationsA2 Substitution
    The whole paper ↗
    June 2022 Paper 3H, question 23: Here are two simultaneous equations. y = x2 + 7x – c and y = 3x + d There is a solution when x = 5 Work out the value of c + d Answer

  8. Q24

    June 2022 · Paper 3H

    4 marksA12 Recognising and sketching graphsA19 Simultaneous equations
    The whole paper ↗
    June 2022 Paper 3H, question 24: Here is a sketch of the graphs of y = k x and y = x2 + c k and c are positive constants. Work out the value of r. r =

  9. Q18

    November 2020 · Paper 1H

    4 marksA19 Simultaneous equations
    The whole paper ↗
    November 2020 Paper 1H, question 18: Solve the simultaneous equations 2x + 4y = –9 2y = 4x – 7 x = y =

  10. Q5

    November 2019 · Paper 3H

    3 marksA19 Simultaneous equations
    The whole paper ↗
    November 2019 Paper 3H, question 5: Solve the simultaneous equations 7x + 2y = 36 3x + 2y = 16 x = y =

  11. Q21

    June 2019 · Paper 1H

    4 marksA19 Simultaneous equations
    The whole paper ↗
    June 2019 Paper 1H, question 21: Solve the simultaneous equations 2x + 3y = 5p y = 2x + p where p is a constant. Give your answers in terms of p in their simplest form. x = y =

  12. Q19

    November 2018 · Paper 1H

    5 marksA21 Forming and solving equationsA19 Simultaneous equations
    The whole paper ↗
    November 2018 Paper 1H, question 19: In a chess club, there are x boys and y girls. 19 (a) If 5 more boys and 8 more girls join, there would be half as many boys as girls. Show that y = 2x + 2 19 (

  13. Q27

    November 2018 · Paper 3H

    8 marksA16 Equation of a circle and tangentsA19 Simultaneous equations
    The whole paper ↗
    November 2018 Paper 3H, question 27: The line y = 3x + p and the circle x2 + y2 = 53 intersect at points A and B. p is a positive integer. 27 (a) Show that the x-coordinates of points A and B satis

  14. Q20

    June 2018 · Paper 1H

    4 marksA25 The nth termA19 Simultaneous equations
    The whole paper ↗
    June 2018 Paper 1H, question 20: A linear sequence starts a + 2b a + 6b a + 10b …….. …….. The 2nd term has value 8 The 5th term has value 44 Work out the values of a and b. a = b =

  15. Q26

    June 2018 · Paper 2H

    4 marksA19 Simultaneous equationsA18 Quadratic equations
    The whole paper ↗
    June 2018 Paper 2H, question 26: A curve has equation y = 4x2 + 5x + 3 A line has equation y = x + 2 Show that the curve and the line have exactly one point of intersection. Do not use a graphi

  16. Q13

    November 2017 · Paper 2H

    1 markA9 Straight-line graphsA19 Simultaneous equations
    The whole paper ↗
    November 2017 Paper 2H, question 13: Two straight lines intersect at point P. Circle the coordinates of P. (–3, –1)       − − 3 1 1, (–1, –3)       − − 1 , 3 1 Not drawn accurately

  17. Q10

    June 2017 · Paper 1H

    3 marksA19 Simultaneous equations
    The whole paper ↗
    June 2017 Paper 1H, question 10: Solve the simultaneous equations. 2x + y = 18 x − y = 6 Answer

  18. Q8

    Specimen · Paper 2H

    3 marksA19 Simultaneous equations
    The whole paper ↗
    Specimen Paper 2H, question 8: Here is the graph of 4x – 3y = 12 for values of x from 0 to 4 3 y 2 O 1 2 3 4 -4 -3 -2 -1 1 x By drawing a second graph on the grid, work out an approximate sol
All 18 questions on Simultaneous equations, as a list
  1. June 2025, Paper 1H, Q1 (3 marks): Solve the simultaneous equations 2x + 5y = 18 2x + y = 6 x = y =
  2. November 2024, Paper 3H, Q24 (5 marks): A curve has the equation y = x2 + 4x – 4 A straight line has the equation y = 3x – 2 Work out the two points of intersection of the curve and the straight line.
  3. June 2024, Paper 1H, Q14 (4 marks): 4 chocolate bars and 3 packets of mints cost £4.70 5 chocolate bars and 1 packet of mints cost £4.50 Work out the cost of a chocolate bar and the cost of a pack
  4. November 2023, Paper 3H, Q11 (3 marks): Solve these simultaneous equations. 7x + 2y = 100 3x + 2y = 48 x = y =
  5. June 2023, Paper 1H, Q16 (4 marks): Solve the simultaneous equations 2x – 5y = 13 3x + 4y = 8 x = y =
  6. November 2022, Paper 1H, Q16 (4 marks): A graph has the equation y = x2 + px + r where p and r are constants. The graph passes through the points (0, 4), (1, 3) and (8, w) Work out the value of w. w =
  7. June 2022, Paper 3H, Q23 (3 marks): Here are two simultaneous equations. y = x2 + 7x – c and y = 3x + d There is a solution when x = 5 Work out the value of c + d Answer
  8. June 2022, Paper 3H, Q24 (4 marks): Here is a sketch of the graphs of y = k x and y = x2 + c k and c are positive constants. Work out the value of r. r =
  9. November 2020, Paper 1H, Q18 (4 marks): Solve the simultaneous equations 2x + 4y = –9 2y = 4x – 7 x = y =
  10. November 2019, Paper 3H, Q5 (3 marks): Solve the simultaneous equations 7x + 2y = 36 3x + 2y = 16 x = y =
  11. June 2019, Paper 1H, Q21 (4 marks): Solve the simultaneous equations 2x + 3y = 5p y = 2x + p where p is a constant. Give your answers in terms of p in their simplest form. x = y =
  12. November 2018, Paper 1H, Q19 (5 marks): In a chess club, there are x boys and y girls. 19 (a) If 5 more boys and 8 more girls join, there would be half as many boys as girls. Show that y = 2x + 2 19 (
  13. November 2018, Paper 3H, Q27 (8 marks): The line y = 3x + p and the circle x2 + y2 = 53 intersect at points A and B. p is a positive integer. 27 (a) Show that the x-coordinates of points A and B satis
  14. June 2018, Paper 1H, Q20 (4 marks): A linear sequence starts a + 2b a + 6b a + 10b …….. …….. The 2nd term has value 8 The 5th term has value 44 Work out the values of a and b. a = b =
  15. June 2018, Paper 2H, Q26 (4 marks): A curve has equation y = 4x2 + 5x + 3 A line has equation y = x + 2 Show that the curve and the line have exactly one point of intersection. Do not use a graphi
  16. November 2017, Paper 2H, Q13 (1 mark): Two straight lines intersect at point P. Circle the coordinates of P. (–3, –1)       − − 3 1 1, (–1, –3)       − − 1 , 3 1 Not drawn accurately
  17. June 2017, Paper 1H, Q10 (3 marks): Solve the simultaneous equations. 2x + y = 18 x − y = 6 Answer
  18. Specimen, Paper 2H, Q8 (3 marks): Here is the graph of 4x – 3y = 12 for values of x from 0 to 4 3 y 2 O 1 2 3 4 -4 -3 -2 -1 1 x By drawing a second graph on the grid, work out an approximate sol

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