Skip to content
Oak National Academy
Oak National Academy
Teachers
Pupils
icon-background-square
New
New
Year 11
Higher

Checking and securing understanding of simultaneous equations

I can recognise that the point of intersection of two linear graphs satisfies both relationships and hence represents the solution to both those equations.

Download all resources
arrow-right
Share activities with pupils
arrow-right
icon-background-square
New
New
Year 11
Higher

Checking and securing understanding of simultaneous equations

I can recognise that the point of intersection of two linear graphs satisfies both relationships and hence represents the solution to both those equations.

Download all resources
arrow-right
Share activities with pupils
arrow-right
warning

These resources will be removed by end of Summer Term 2025.

Switch to our new teaching resources now - designed by teachers and leading subject experts, and tested in classrooms.

These resources were created for remote use during the pandemic and are not designed for classroom teaching.

View new resources
arrow-right

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

  • Simultaneous equations - Equations which represent different relationships between the same variables are called simultaneous equations.

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

Common misconception

Pupils may mix-up the x and y coordinates.

Remind pupils that the x value is read from the x-axis and is read first. The y value is read from the y-axis and is read second.


To help you plan your year 11 maths lesson on: Checking and securing understanding of simultaneous equations, download all teaching resources for free and adapt to suit your pupils' needs...

Give pupils more equations with fractional gradients and ask them to create a useful table of values for plotting. What x values should be chosen to generate integer co-ordinates? Can pupils generalise a rule?
speech-bubble
Teacher tip
copyright

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

Loading...

Starter quiz

Download starter quiz

6 Questions

Q1.
Which of these are solutions to the equation $$y=3x-4$$?
$$x=0, y=3$$
Correct answer: $$x=2, y=2$$
$$x=5, y=19$$
$$x=8, y=18$$
Correct answer: $$x=10, y=26$$
Q2.
What is the gradient of the line with equation $$y=4x+2$$ ?
Correct Answer: 4, four
Q3.
What is the gradient of the line with equation $$2y+5x=10$$ ?
2
5
10
$$-\frac{2}{5}$$
Correct answer: $$-\frac{5}{2}$$
Q4.
What is the $$x$$ intercept of the line with equation $$3y+4x=12$$ ?
(0, 3)
(0, 4)
Correct answer: (3, 0)
(4, 0)
Q5.
Fill in the missing coordinate for the $$y$$ intercept of the line with equation $$3y+4x=12$$ (0, )
Correct Answer: 4
Q6.
Which of these shows the line with equation $$2y=6-4x$$ ?
An image in a quiz
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz

Exit quiz

Download exit quiz

6 Questions

Q1.
The __________ shows us a value of $$x$$ and $$y$$ that satisfies two linear equations simultaneously when plotted.
gradient
$$x$$-intercept
$$y$$-intercept
Correct answer: point of intersection
Q2.
Here are the lines with equations $$y=2x+1$$ and $$y=5-2x$$. What is the solution to both equations simultaneously?
An image in a quiz
$$x=0, y=1$$
Correct answer: $$x=1, y=3$$
$$x=2.5, y=0$$
$$x=3, y=1$$
Q3.
How many solutions are there to the equations $$y=2x+8$$ and $$y=2x+3$$ when solved simultaneously?
Correct answer: none
one
two
infinite
Q4.
How many solutions are there to the equations $$2y=3x+4$$ and $$4y-6x=8$$ when solved simultaneously?
none
one
two
Correct answer: infinite
Q5.
Here is the line with equation $$y=x-1$$. What is the solution to the simultaneous equations $$y=x-1$$ and $$y=2x-4$$?
An image in a quiz
$$x=0, y=-4$$
$$x=1, y=0$$
$$x=2, y=1$$
Correct answer: $$x=3, y=2$$
$$x=4, y=5$$
Q6.
Here is the line with equation $$y=x-1$$. What is the solution to the simultaneous equations $$y=x-1$$ and $$3y+2x=12$$?
An image in a quiz
$$x=0, y=-1$$
$$x=1, y=0$$
$$x=2, y=1$$
Correct answer: $$x=3, y=2$$
$$x=4, y=3$$