10 questions🇬🇧English

🔀 Simultaneous Equations – GCSE

Maths · GCSE — solving linear simultaneous equations by elimination, substitution and from word problems

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Questions

Solve the simultaneous equations x + y = 10 and x − y = 4. What are x and y?

x = 8, y = 2

x = 7, y = 3

x = 3, y = 7

x = 6, y = 4

20s

To eliminate y from 2x + 3y = 12 and 4x − 3y = 6, what should you do with the two equations?

Multiply the first equation by 2

Add the equations

Divide the second equation by 3

Subtract the equations

20s

Which pair of values satisfies both y = 2x and x + y = 9?

x = 6, y = 3

x = 2, y = 4

x = 4, y = 5

x = 3, y = 6

20s

Use substitution to solve y = x + 2 and 3x + y = 18. What are x and y?

x = 5, y = 7

x = 4, y = 6

x = 5, y = 3

x = 6, y = 4

30s

To eliminate x from 3x + 2y = 16 and x + 5y = 14, which is the correct first step?

Multiply the second by 5, then subtract

Multiply the first by 3, then subtract

Multiply the second by 3, then subtract

Multiply the second by 3, then add

30s

At which point do the lines y = 2x + 1 and y = −x + 7 intersect?

(5, 2)

(2, 5)

(−2, 9)

(3, 7)

30s

3 pens and 2 pencils cost £1.30. 1 pen and 2 pencils cost 70p. How much does one pen cost?

20p

35p

30p

60p

30s

Adult tickets cost £5 and child tickets cost £3. A group buys 10 tickets for £38. How many adult tickets did they buy?

4

5

6

3

30s

Solve 3x + 4y = 10 and 2x − 3y = 1. What are x and y?

x = −2, y = 4

x = 1, y = 2

x = 5, y = 3

x = 2, y = 1

60s

How many solutions do the simultaneous equations y = 3x + 2 and 6x − 2y = 5 have?

No solutions

Exactly one solution

Infinitely many solutions

Exactly two solutions

30s