Robinson Tuition
Grade 5 · Foundation and Higher · free GCSE maths worksheet

Solving simultaneous equations with elimination

Linear pairs of equations.

14 original questions, 52 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

Solve the simultaneous equations

x + y = 11

x - y = 3

3 marks
Show answer
x = 7, y = 4
2

Solve the simultaneous equations

3x + y = 17

x + y = 7

3 marks
Show answer
x = 5, y = 2
3

Solve the simultaneous equations

2x + 3y = 12

2x + y = 8

3 marks
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x = 3, y = 2
4

Solve the simultaneous equations

4x - y = 14

2x + y = 10

3 marks
Show answer
x = 4, y = 2
5

Solve the simultaneous equations

3x + 2y = 19

x + 4y = 13

3 marks
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x = 5, y = 2
6

Solve the simultaneous equations

x + 2y = 4

3x + 5y = 9

3 marks
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x = -2, y = 3
7

Solve the simultaneous equations

  5x + 2y = 4

  3x − 4y = 18

4 marks
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a) x = 2 b) y = -3
8

Solve the simultaneous equations

3x + 2y = 24

2x + 5y = 27

4 marks
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x = 6, y = 3
9

Solve the simultaneous equations

4x + 3y = 5

6x - 2y = 14

4 marks
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x = 2, y = -1
10

Solve the simultaneous equations

  3x − 2y = 13

  5x − 3y = 21

4 marks
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a) x = 3 b) y = -2
11

Solve the simultaneous equations

  2x + 3y = 4

  4x + 5y = 7

4 marks
Show answer
a) x = 0.5 (1/2) b) y = 1
12

Solve the simultaneous equations

6x + 5y = 10

4x - 3y = 13

4 marks
Show answer
x = 2.5, y = -1
13

A theatre sells adult tickets and child tickets.

2 adult tickets and 3 child tickets cost £36.50

3 adult tickets and 2 child tickets cost £38.50

Work out the cost of one adult ticket and the cost of one child ticket.

5 marks
Show answer
a) £8.50 b) £6.50
14

A cafe sells teas and coffees.

3 teas and 2 coffees cost £7.80

2 teas and 3 coffees cost £8.20

Work out the cost of one tea and the cost of one coffee.

5 marks
Show answer
tea) £1.40 coffee) £1.80

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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