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Simultaneous equations practice questions with answers

Foundation and Higher · Grade 5 · Non-calculator

A second set of simultaneous equations questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

More questions

Question 1 Easy

Solve 5x+y=12 and 2x+y=6.

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Answer: x=2, y=2

  1. Subtract equations: 3x = 6, so x = 2.
  2. Substitute: 2(2) + y = 6 gives y = 2.
  • Method (1): Subtract equations: 3x = 6, so x = 2.
  • Accuracy (1): Substitute: 2(2) + y = 6 gives y = 2.

Question 2 Easy

Solve x+y=5 and 2x+y=8.

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Answer: x=3, y=2

  1. Subtract equations: x = 3.
  2. Substitute: 3 + y = 5 gives y = 2.
  • Method (1): Subtract equations: x = 3.
  • Accuracy (1): Substitute: 3 + y = 5 gives y = 2.

Question 3 Medium

Solve 2x+y=7 and x+y=4, and give only y.

Show answer

Answer: 1

  1. Subtract to get x = 3.
  2. Substitute x = 3 into x + y = 4: y = 1.
  • Method (1): Subtract to get x = 3.
  • Accuracy (1): Substitute x = 3 into x + y = 4: y = 1.

Question 4 Medium

Solve 3x+2y=16 and x+2y=8, and give only y.

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Answer: 2

  1. Subtract to get 2x = 8, so x = 4.
  2. Substitute: 4 + 2y = 8, so 2y = 4 and y = 2.
  • Method (1): Subtract to get 2x = 8, so x = 4.
  • Accuracy (1): Substitute: 4 + 2y = 8, so 2y = 4 and y = 2.

Question 5 Hard

Solve 4x + y = 18 and 2x + y = 10.

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Answer: x=4, y=2

  1. Subtract: 2x = 8, so x = 4.
  2. Then y = 10 − 8 = 2.
  • Method (1): Subtract: 2x = 8, so x = 4.
  • Accuracy (1): Then y = 10 − 8 = 2.

Question 6 Hard

Solve 5x + y = 17 and 2x + y = 8.

Show answer

Answer: x=3, y=2

  1. Subtract: 3x = 9, so x = 3.
  2. Then y = 8 − 6 = 2.
  • Method (1): Subtract: 3x = 9, so x = 3.
  • Accuracy (1): Then y = 8 − 6 = 2.

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 13 marks

Solve 3x+y=11 and 2x+y=8, and give only y.

Show answer

Answer: 2

  1. Subtract equations to eliminate y: x = 3.
  2. Substitute x = 3 into 2x + y = 8 to get y = 8 - 6 = 2.
  • Method (1): Subtracts the equations to eliminate y: x = 3
  • Method (1): Substitutes x = 3 into an equation: 2(3) + y = 8
  • Accuracy (1): 2

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

To eliminate y from 2x + y = 7 and x + y = 4, what should you do?

  1. Subtract the equations
  2. Add the equations
  3. Multiply the equations
Show answer

Subtract the equations Subtracting eliminates the identical +y terms.

Check 2

Solve 2x+y=7 and x+y=4 for x:

  1. x = 3
  2. x = 1
  3. x = 4
Show answer

x = 3 2x - x = 7 - 4 = 3.

Check 3

If x = 3 and x + y = 4, what is y?

  1. 1
  2. 7
  3. 3
Show answer

1 3 + y = 4 implies y = 1.

Check 4

What is the solution pair to 4x+y=9 and 2x+y=5?

  1. x=2, y=1
  2. x=1, y=2
  3. x=2, y=5
Show answer

x=2, y=1 2x = 4 so x = 2, then y = 1.

Check 5

What is the solution pair to x+y=5 and 2x+y=8?

  1. x=3, y=2
  2. x=2, y=3
  3. x=4, y=1
Show answer

x=3, y=2 x = 8 - 5 = 3, so y = 2.

Check 6

Solve 3x+2y=16 and x+2y=8, giving only x:

  1. 4
  2. 2
  3. 8
Show answer

4 2x = 8, so x = 4.

Check 7

Solve 3x+2y=16 and x+2y=8, giving only y:

  1. 2
  2. 4
  3. 6
Show answer

2 x = 4, so 4 + 2y = 8, y = 2.

Check 8

Solve 4x+y=9 and 2x+y=5, giving only x:

  1. 2
  2. 1
  3. 4
Show answer

2 2x = 4, so x = 2.

Check 9

What is 2x+3y added to 4x+5y?

  1. 6x+8y
  2. 8x+15y
  3. 6x+15y
Show answer

6x+8y (2+4)x + (3+5)y = 6x+8y.

Check 10

What is 3x+2y added to 5x+4y?

  1. 8x+6y
  2. 15x+8y
  3. 8x+8y
Show answer

8x+6y (3+5)x + (2+4)y = 8x+6y.

Check 11

What is 4x+2y added to 3x+5y?

  1. 7x+7y
  2. 12x+10y
  3. 7x+10y
Show answer

7x+7y (4+3)x + (2+5)y = 7x+7y.

Check 12

What is 2x+6y added to 5x+y?

  1. 7x+7y
  2. 10x+6y
  3. 7x+6y
Show answer

7x+7y (2+5)x + (6+1)y = 7x+7y.

Check 13

How can you check your solution to simultaneous equations?

  1. Substitute both values into both original equations
  2. Check only the first equation
  3. Graph only one line
Show answer

Substitute both values into both original equations A true solution must satisfy both equations simultaneously.

Check 14

If coefficients of y have opposite signs, e.g. +y and -y, how do you eliminate y?

  1. Add the equations
  2. Subtract the equations
  3. Multiply the equations
Show answer

Add the equations Adding +y and -y eliminates the y term.

Check 15

What does the solution to simultaneous equations represent graphically?

  1. The point where the two lines intersect
  2. The y-intercept of the lines
  3. The distance between the lines
Show answer

The point where the two lines intersect The coordinates (x, y) satisfy both line equations.

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