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Lesson 8 of 10
  • Year 10
  • Foundation

Solving simultaneous linear equations graphically

I can solve two linear simultaneous equations graphically (0 or 1 or infinitely many solutions).

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View unit
Lesson 8 of 10
New
New
  • Year 10
  • Foundation

Solving simultaneous linear equations graphically

I can solve two linear simultaneous equations graphically (0 or 1 or infinitely many solutions).

Download all

These resources were made for remote use during the pandemic, not classroom teaching.

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Lesson details

Key learning points

  1. You can use your knowledge of linear graphs to draw the graphs of both equations on the same axes.
  2. If there exists a solution, the point of intersection is that solution.
  3. If the lines are parallel then there are no solutions.
  4. If the lines lie on top of each other, there are infinitely many solutions.

Keywords

  • Linear - The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed.

Common misconception

Equations always have one solution.

Some equations have one solution but, some have no solutions, some have two solutions, some have more than two solutions.


To help you plan your year 10 maths lesson on: Solving simultaneous linear equations graphically, download all teaching resources for free and adapt to suit your pupils' needs...

If you have access to technology, encourage pupils to explore graphing and see if they can come up with their own equations which have no solutions and ones which have infinitely many solutions.
Teacher tip

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Prior knowledge starter quiz

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6 Questions

Q1.
Using substitution, what is the value of $$x$$ for simultaneous equations $$6x + 4y = 32$$ and $$x + 3y = 17$$?

Correct Answer: 2, x = 2

Q2.
Using substitution, what is the value of $$x$$ for simultaneous equations $$6x + 4y = 64$$ and $$x + 3y = 34$$?

Correct Answer: 4, x = 4

Q3.
Using substitution, what is the value of $$y$$ for simultaneous equations $$10x + 8y = 56$$ and $$x + 3y = 10$$?

Correct Answer: 2, y = 2

Q4.
Using substitution, what is the value of $$y$$ for simultaneous equations $$14x + 4y = 6$$ and $$2x = 3 - y$$?

Correct Answer: 5, y = 5

Q5.
Using substitution, what is the value of $$y$$ for simultaneous equations $$14x + 4y = 72$$ and $$2x + y = 15$$?

Correct Answer: 11, y = 11

Q6.
Using substitution, what is the value of $$y$$ for simultaneous equations $$2y - 2x = -2$$ and $$3x + y = 19$$?

Correct Answer: 4, y = 4

Assessment exit quiz

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6 Questions

Q1.
If A and B are simultaneous equations such that A: $$x + 2y = 21$$ and B: $$3x + y = 43$$ where will coordinate pair $$(1, 10)$$ go in the Venn diagram?

An image in a quiz
Correct answer: In A but not B
In B but not A
The intersection of A and B
Outside of both A and B

Q2.
If A and B are simultaneous equations such that A: $$2x + 2y = 10$$ and B: $$3x + y = 7$$ where will coordinate pair $$(1, 4)$$ go in the Venn diagram?

An image in a quiz
In A but not B
In B but not A
Correct answer: The intersection of A and B
Outside of both A and B

Q3.
If A and B are simultaneous equations such that A: $$2y - 2x = 8$$ and B: $$3x + y = 4$$ where will coordinate pair $$(0, 0)$$ go in the Venn diagram?

An image in a quiz
In A but not B
In B but not A
The intersection of A and B
Correct answer: Outside of both A and B

Q4.
If A and B are simultaneous equations such that A: $$3x + y = 40$$ and B: $$7x + y = 88$$ where will coordinate pair $$(12, 4)$$ go in the Venn diagram?

An image in a quiz
In A but not B
In B but not A
Correct answer: The intersection of A and B
Outside of both A and B

Q5.
If A and B are simultaneous equations such that A: $$3x + y = 13$$ and B: $$7x + 6y = 34$$ where will coordinate pair $$(5, -2)$$ go in the Venn diagram?

An image in a quiz
Correct answer: In A but not B
In B but not A
The intersection of A and B
Outside of both A and B

Q6.
If A and B are simultaneous equations such that A: $$3x + y = 9$$ and B: $$4x +3y = 7$$ where will coordinate pair $$(1, 1)$$ go in the Venn diagram?

An image in a quiz
In A but not B
Correct answer: In B but not A
The intersection of A and B
Outside of both A and B