BREAKING
Student finds x, x refuses to elaborate★Paper 1 still non-calculator, nation in shock★Local teen shows working, examiner weeps with joy★
  1. Home
  2. IGCSE
  3. Mathematics
  4. Edexcel
  5. Simultaneous equations

Edexcel IGCSE Maths

Topic questions Pure mathematics Simultaneous equations

Simultaneous equations

53 questions · 227 marks · about 4.5 hours

Simultaneous equations questions

TopicSimultaneous equations

Edexcel 4MA1 Simultaneous equations 53 questions

Paper 1F June 2025 (R) Foundation tier, Question 6 4 marks

Aabir has some boxes and some crates. Each box has the same weight. Each crate has the same weight.

The total weight of 7 boxes and 2 crates is 27.3 kg The total weight of 4 boxes and 2 crates is 16.8 kg

Work out the weight of one crate.

[4]
Reveal mark scheme Mark scheme for question 6

Paper 1H June 2025 Higher tier, Question 22 5 marks

Solve the simultaneous equations

Question 22, shown as an image

y = x + 2

Show clear algebraic working.

[5]
Reveal mark scheme Mark scheme for question 22

Paper 1H June 2025 (R) Higher tier, Question 24 6 marks

Also involves Forming and solving equations

The first 3 terms of an arithmetic series are

(2x + 5) (3y – 4) (4x – 2)

where x and y are constants.

The sum of the first 9 terms of the series is 216

Find the value of x and the value of y Show clear algebraic working.

[6]
Reveal mark scheme Mark scheme for question 24

Paper 2F June 2025 (R) Foundation tier, Question 19, also on the Higher paper 3 marks

Solve the simultaneous equations

Question 19, shown as an image

Show clear algebraic working.

[3]
Reveal mark scheme Mark scheme for question 19

Paper 2F June 2025 Foundation tier, Question 25, also on the Higher paper 3 marks

Solve the simultaneous equations

3 x + 5 y = 8 4 x + y = –3.5

Show clear algebraic working.

[3]
Reveal mark scheme Mark scheme for question 25

Paper 2H June 2025 Higher tier, Question 8, also on the Foundation paper 3 marks

Solve the simultaneous equations

3 x + 5 y = 8 4 x + y = – 3.5

Show clear algebraic working.

[3]
Reveal mark scheme Mark scheme for question 8

Paper 1H June 2024 (R) Higher tier, Question 12 4 marks

Solve the simultaneous equations

4x + 3y = 9.6 6x + 5y = 16.8

Show clear algebraic working.

[4]
Reveal mark scheme Mark scheme for question 12

Paper 2H November 2023 Higher tier, Question 14 3 marks

Also involves Straight line graphs

14Here is the graph of the equation 2y maths symbol x maths symbol1 drawn on a grid.

Figure for question 14

By drawing another straight line on the grid, solve the simultaneous equations

Question 14, shown as an image
[3]
Reveal mark scheme Mark scheme for question 14

Paper 2H November 2023 Higher tier, Question 21 5 marks

Also involves Substitution into formulae

21The line with equation x maths symbol 2y maths symbol 5 intersects the curve with equation x2 maths symbol 3y2 maths symbol13 at the points A and B

Find the coordinates of A and the coordinates of B Show clear algebraic working.

[5]
Reveal mark scheme Mark scheme for question 21

Paper 1F June 2023 Foundation tier, Question 24, also on the Higher paper 3 marks

Solve the simultaneous equations

2x + 9y = 14.5 7x + 3y = 8

Show clear algebraic working.

[3]
Reveal mark scheme Mark scheme for question 24

Paper 1F June 2023 (R) Foundation tier, Question 28, also on the Higher paper 5 marks

Moeen has a biased 6-sided dice.

The table gives information about the probability that, when the dice is thrown, it will land on each number.

Number123456
Probabilityx0.150.5y0.130.03
(a)

Show that x + y = 0.19

[2]
Reveal mark scheme Mark scheme for question 28(a)
(b)

Given that 3x – y = 0.09

and x + y = 0.19

work out the value of x and the value of y Show clear algebraic working.

[3]
Reveal mark scheme Mark scheme for question 28(b)

Paper 1H June 2023 Higher tier, Question 9, also on the Foundation paper 3 marks

Solve the simultaneous equations

2x + 9y = 14.5 7x + 3y = 8

Show clear algebraic working.

[3]
Reveal mark scheme Mark scheme for question 9

Paper 1H June 2023 (R) Higher tier, Question 12, also on the Foundation paper 5 marks

Moeen has a biased 6-sided dice.

The table gives information about the probability that, when the dice is thrown, it will land on each number.

Number123456
Probabilityx0.150.5y0.130.03
(a)

Show that x + y = 0.19

[2]
Reveal mark scheme Mark scheme for question 12(a)
(b)

Given that 3x – y = 0.09

and x + y = 0.19

work out the value of x and the value of y Show clear algebraic working.

[3]
Reveal mark scheme Mark scheme for question 12(b)

Paper 2H June 2023 Higher tier, Question 21 5 marks

Solve the simultaneous equations

2x2 + 3y2 = 11 x = 3y – 1

Show clear algebraic working.

[5]
Reveal mark scheme Mark scheme for question 21

Paper 1F January 2023 (R) Foundation tier, Question 21, also on the Higher paper 3 marks

Solve the simultaneous equations

x + 2 y = 15 4 x – 6 y = 4

Show clear algebraic working.

[3]
Reveal mark scheme Mark scheme for question 21

Paper 1H January 2023 (R) Higher tier, Question 6, also on the Foundation paper 3 marks

Solve the simultaneous equations

x + 2 y = 15 4 x – 6 y = 4

Show clear algebraic working.

[3]
Reveal mark scheme Mark scheme for question 6

Paper 2F January 2023 Foundation tier, Question 22, also on the Higher paper 3 marks

Solve the simultaneous equations

5 x + 4 y = –2 2 x – y = 4.4

Show clear algebraic working.

[3]
Reveal mark scheme Mark scheme for question 22

Paper 2H January 2023 Higher tier, Question 7, also on the Foundation paper 3 marks

Solve the simultaneous equations

5 x + 4 y = –2 2 x – y = 4.4

Show clear algebraic working.

[3]
Reveal mark scheme Mark scheme for question 7

Paper 2H January 2023 (R) Higher tier, Question 25 6 marks

ABCD is a trapezium with AB parallel to DC

A is the point with coordinates (–4, 6) B is the point with coordinates (2, 3) D is the point with coordinates (–1, 8)

The trapezium has one line of symmetry. The line of symmetry intersects CD at the point E

Work out the coordinates of the point E

[6]
Reveal mark scheme Mark scheme for question 25

Paper 1H June 2022 (R) Higher tier, Question 14 4 marks

Solve the simultaneous equations

3 x – 5 y = 25 4 x + 3 y = 14

Show clear algebraic working.

[4]
Reveal mark scheme Mark scheme for question 14

Paper 2H January 2022 Higher tier, Question 10 3 marks

Solve the simultaneous equations

3 x + 5 y = 3.1 6 x + 3 y = 3.75

Show clear algebraic working.

[3]
Reveal mark scheme Mark scheme for question 10

Paper 2H January 2022 (R) Higher tier, Question 18 5 marks

The line with equation 2 y = x + 1 intersects the curve with equation 3y2 + 7y + 16 = x2 – x at the points A and B

Find the coordinates of A and the coordinates of B Show clear algebraic working.

(........ ,........ ) and (........ ,........

[5]
Reveal mark scheme Mark scheme for question 18

Paper 2H January 2022 (R) Higher tier, Question 22 5 marks

Also involves Coordinate geometry

ABC is a triangle in which angle ABC = 90°

p and q are integers such that

the coordinates of A are (p, 10) the coordinates of B are (–1, –5) the coordinates of C are (8, q)

Given that the gradient of AC is – fraction

work out the value of p and the value of q

[5]
Reveal mark scheme Mark scheme for question 22

Paper 1F November 2021 Foundation tier, Question 17, also on the Higher paper 5 marks

Also involves Forming and solving equations

Yasmin has some identical rectangular tiles. Each tile is Lcm by Wcm.

Diagram NOT L cm accurately drawn

W cm

Using 9 of her tiles, Yasmin makes rectangle ABCD shown in the diagram below.

Figure for question 17

The area of ABCD is 1620 cm2

Work out the value of L and the value of W.

L =........ W =........

[5]
Reveal mark scheme Mark scheme for question 17

Paper 1F November 2021 Foundation tier, Question 18, also on the Higher paper 5 marks

Alison buys 5 apples and 3 pears for a total cost of $1.96 Greg buys 3 apples and 2 pears for a total cost of $1.22

Michael buys 10 apples and 10 pears.

Work out how much Michael pays for his 10 apples and 10 pears. Show your working clearly.

[5]
Reveal mark scheme Mark scheme for question 18

Paper 1H November 2021 Higher tier, Question 5, also on the Foundation paper 5 marks

Also involves Forming and solving equations

Yasmin has some identical rectangular tiles. Each tile is Lcm by Wcm.

Diagram NOT L cm accurately drawn

W cm

Using 9 of her tiles, Yasmin makes rectangle ABCD, shown in the diagram below.

Figure for question 5

The area of ABCD is 1620 cm2

Work out the value of L and the value of W.

L =........ W =........

[5]
Reveal mark scheme Mark scheme for question 5

Paper 1H November 2021 Higher tier, Question 6, also on the Foundation paper 5 marks

Alison buys 5 apples and 3 pears for a total cost of $1.96 Greg buys 3 apples and 2 pears for a total cost of $1.22

Michael buys 10 apples and 10 pears.

Work out how much Michael pays for his 10 apples and 10 pears. Show your working clearly.

[5]
Reveal mark scheme Mark scheme for question 6

Paper 1H January 2021 Higher tier, Question 18 3 marks

Question 18, shown as an image

find the value of x and the value of y. Show each stage of your working clearly.

[3]
Reveal mark scheme Mark scheme for question 18

Paper 2H January 2021 (R) Higher tier, Question 12 4 marks

Solve the simultaneous equations 2 x + 7 y = 17 5x + 3y = –1 Show clear algebraic working.

[4]
Reveal mark scheme Mark scheme for question 12

Paper 1H November 2020 Higher tier, Question 12 4 marks

Solve the simultaneous equations

7 x – 2 y = 34 3 x + 5 y = −3

Show clear algebraic working.

[4]
Reveal mark scheme Mark scheme for question 12

Paper 1H November 2020 (R) Higher tier, Question 12 4 marks

Solve the simultaneous equations

7 x + 2 y = 5.5 3 x – 5 y = 17

Show clear algebraic working.

[4]
Reveal mark scheme Mark scheme for question 12

Paper 2F November 2020 Foundation tier, Question 21 6 marks

(a)

Simplify g6 maths symbol g4

[1]
(b)

Simplify (3cd4)2

[2]
(c)

Solve the simultaneous equations

4 x + 3 y = 17 x + 2 y = 5

Show clear algebraic working.

[3]
Reveal mark scheme Mark scheme for question 21(c)

Paper 1H January 2020 Higher tier, Question 22 6 marks

Question 22, shown as an image

H is the point with coordinates (−4, 1) J is the point with coordinates (j, 15) where j <0 K is the point with coordinates (6, k)

M is the midpoint of JK. The gradient of HM is 2

Find the value of j and the value of k.

[6]
Reveal mark scheme Mark scheme for question 22

Paper 2H January 2020 (R) Higher tier, Question 7 3 marks

Solve the simultaneous equations 3 x + 5 y = 6 7x – 5y = –11 Show clear algebraic working.

[3]
Reveal mark scheme Mark scheme for question 7

Paper 2H June 2019 Higher tier, Question 9 3 marks

Solve the simultaneous equations

x + 2ymaths symbol

3 x – y = 16

Show clear algebraic working.

[3]
Reveal mark scheme Mark scheme for question 9

Paper 2H June 2019 Higher tier, Question 20 5 marks

The equation of the line L is ymaths symbolx The equation of the curve C is x2maths symbolxy + 2y2 = 0

L and C intersect at two points.

Find the coordinates of these two points. Show clear algebraic working.

(........ ,........ ) and (........ ,........

[5]
Reveal mark scheme Mark scheme for question 20

Paper 1H June 2018 Higher tier, Question 12 4 marks

Also involves Straight line graphs

The diagram shows two straight lines drawn on a grid.

Figure for question 12
(a)

Write down the solution of the simultaneous equations

3 y = 2 x + 6 4 x + 3 y = 24

[1]
(b)

Show, by shading on the grid, the region defined by all five of the inequalities

Label the region R.

[3]
Reveal mark scheme Mark scheme for question 12(b)

Paper 2F June 2018 Foundation tier, Question 23, also on the Higher paper 3 marks

Solve the simultaneous equations

x + y = 15 7 x – 5 y = 3

Show clear algebraic working.

[3]
Reveal mark scheme Mark scheme for question 23

Paper 2H June 2018 Higher tier, Question 9, also on the Foundation paper 3 marks

Solve the simultaneous equations

x + y = 15 7 x – 5 y = 3

Show clear algebraic working.

[3]
Reveal mark scheme Mark scheme for question 9

Report a problem with a question on this page
What is wrong?

Goes to whoever maintains the question split. No account needed and nothing is published on this page.

Memes

Certified Maths memes. Peer-reviewed by nobody.

Laugh now. Cry in the exam hall later. Then come back and do a past paper.

Learn the formula
Draw a vague triangle and hope
Me with 4 minutes left on Paper 3
Using a calculator
Using the formula sheet
Doing it in your head
Writing ‘by inspection’ and walking out
Maths enlightenment, ranked

Mum 💖

did you do your maths homework sweetie?? 🥰

yes I solved for x

proud of you!!!

📱 Screen time this week · TikTok6h 7m

x was never found

Maths starter pack

Protractor you've never usedCalculator older than you“Show your working” traumaThis website
Collect all four