New

Solving simultaneous linear equations graphically

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

Download all

View unit

Lesson 8 of 13

New

Year 10

Solving simultaneous linear equations graphically

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

Download all

Lesson slides

Download lesson slides

Skip lesson slides

Lesson details

Key learning points

You can use your knowledge of linear graphs to draw the graphs of both equations on the same axes.
If there exists a solution, the point of intersection is that solution.
If the lines are parallel then there are no solutions.
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.

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

Skip lesson video

Worksheet

Download worksheet

Skip worksheet

Prior knowledge starter quiz

Download quiz pdf

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

Download quiz pdf

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?

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?

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?

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?

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?

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?

In A but not B

Correct answer: In B but not A

The intersection of A and B

Outside of both A and B

Lesson appears in

UnitMaths / Simultaneous equations: 2 variables

Maths

Show Foundation unit

Show Higher unit

Choose exam board for KS4 Biology

Choose exam board for KS4 Chemistry

Choose exam board for KS4 Combined science

Choose exam board for KS4 Computer Science (GCSE)

Choose exam board for KS4 English

Choose exam board for KS4 French

Choose exam board for KS4 Geography

Choose exam board for KS4 German

Choose exam board for KS4 History

Choose tier for KS4 Maths

Choose exam board for KS4 Music

Choose exam board for KS4 Physical education (GCSE)

Choose exam board for KS4 Physics

Choose exam board for KS4 Religious education (GCSE)

Choose exam board for KS4 Spanish

Solving simultaneous linear equations graphically

Solving simultaneous linear equations graphically

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

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

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

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

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

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

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

Assessment exit quiz

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?

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?

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?

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?

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?

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?

Lesson appears in

UnitMaths / Simultaneous equations: 2 variables

Maths

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

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

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

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

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

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

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?

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?

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?

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?

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?

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?