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Year 11
Foundation

Non-solutions to simultaneous linear equations

I can identify what happens to the equations when a point other than the intersection is substituted into the equations.

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New
New
Year 11
Foundation

Non-solutions to simultaneous linear equations

I can identify what happens to the equations when a point other than the intersection is substituted into the equations.

Download all resources
Share activities with pupils

Link copied to clipboard

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

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Lesson details

Key learning points

  1. If a point on neither line is substituted into the equations, neither equation will be valid
  2. If a point on one of the lines is substituted into the equations, one equation will be valid
  3. Depending on the location of the point, the equation may evaluate to a bigger or smaller value
  4. Replacing the equals sign with an inequality sign would make the statement true

Keywords

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

  • Inequality - An inequality is used to show that one expression may not be equal to another.

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: Non-solutions to simultaneous linear equations, download all teaching resources for free and adapt to suit your pupils' needs...

If pupils are a little uncertain over declaring whether the y value is greater than or smaller than the value of the expression then you may wish to encourage pupils to check their answer with the graph and the inequality statement.
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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Starter quiz

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6 Questions

Q1.
Match up the inequalities to the statements.
Correct Answer:$$x<3$$,values less than 3

values less than 3

Correct Answer:$$x\le3$$,values less than or equal to 3

values less than or equal to 3

Correct Answer:$$x>3$$,values greater than 3

values greater than 3

Correct Answer:$$x\ge3$$,values greater than or equal to 3

values greater than or equal to 3

Q2.
Which of these are valid inequalities?
Correct answer: $$3<5$$
$$2<-2$$
$$-2>-1$$
Correct answer: $$-5<-3$$
$$-4>0$$
Q3.
Which of these solutions satisfy the equation $$y=3x-1$$?
$$x=-3 , y=-8$$
$$x=0 , y=2$$
Correct answer: $$x=2 , y=5$$
$$x=5 , y=10$$
$$x=8 , y=21$$
Q4.
Which of these coordinates are on the line with equation $$y=2x+5$$?
(-5, -15)
Correct answer: (-3, -1)
(0, 2)
(4, 28)
Correct answer: (7, 19)
Q5.
Using the graph or otherwise, what is the solution to the equations $$y=2x+5$$ and $$y=2-x$$ simultaneously?
An image in a quiz
$$x=-2, y=4$$
Correct answer: $$x=-1, y=3$$
$$x=0, y=5$$
$$x=1, y=3$$
$$x=2, y=0$$
Q6.
Which of these equations is $$x=5, y=3$$ a solution to?
Correct answer: $$y=13-2x$$
$$y=x+2$$
$$y=2x+7$$
$$y=3x-6$$
Correct answer: $$y=4x-17$$

Exit quiz

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6 Questions

Q1.
Which of these coordinates satisfy the inequality $$y>2x$$?
Correct answer: (0, 3)
(1, 1)
Correct answer: (2, 5)
(3, 4)
(6, 10)
Q2.
Using the graph of $$y=5-2x$$ (or otherwise) which coordinates satisfy the inequality $$y<5-2x$$?
An image in a quiz
Correct answer: (-2, 3)
(0, 6)
Correct answer: (1, 2)
(2, 3)
(3, 0)
Q3.
Match the solutions to the descriptions. Use the graphs to help you.
An image in a quiz
Correct Answer:$$x=-2, y=2$$,Solution to $$y=\frac{1}{2}x+3$$ but not a solution to $$y=3x-2$$

Solution to $$y=\frac{1}{2}x+3$$ but not a solution to $$y=3x-2$$

Correct Answer:$$x=1, y=1$$,Solution to $$y=3x-2$$ but not a solution to $$y=\frac{1}{2}x+3$$

Solution to $$y=3x-2$$ but not a solution to $$y=\frac{1}{2}x+3$$

Correct Answer:$$x=2, y=4$$,Solution to both $$y=3x-2$$ and $$y=\frac{1}{2}x+3$$ simultaneously

Solution to both $$y=3x-2$$ and $$y=\frac{1}{2}x+3$$ simultaneously

Correct Answer:$$x=5, y=5$$,Not a solution to $$y=3x-2$$ nor a solution to $$y=\frac{1}{2}x+3$$

Not a solution to $$y=3x-2$$ nor a solution to $$y=\frac{1}{2}x+3$$

Q4.
Which statements are true for the point (2, 3)?
An image in a quiz
Correct answer: $$y<2x+1$$
$$y>2x+1$$
$$y<5-2x$$
Correct answer: $$y>5-2x$$
Q5.
Match the coordinates to the correct statements.
An image in a quiz
Correct Answer:(-3, 3),$$y>2x+5$$ and $$y<2-x$$

$$y>2x+5$$ and $$y<2-x$$

Correct Answer:(-2, 4),$$y>2x+5$$ and $$y=2-x$$

$$y>2x+5$$ and $$y=2-x$$

Correct Answer:(-1, 2),$$y<2x+5$$ and $$y<2-x$$

$$y<2x+5$$ and $$y<2-x$$

Correct Answer:(0, 5),$$y=2x+5$$ and $$y>2-x$$

$$y=2x+5$$ and $$y>2-x$$

Correct Answer:(1, 1),$$y<2x+5$$ and $$y=2-x$$

$$y<2x+5$$ and $$y=2-x$$

Correct Answer:(2, 2),$$y<2x+5$$ and $$y>2-x$$

$$y<2x+5$$ and $$y>2-x$$

Q6.
Which coordinate pair satisfies the inequalities $$y>x-1$$ and $$y<2x-1$$?
An image in a quiz
(-2, 2)
(0, 3)
(2, 6)
Correct answer: (3, 4)
(4, 1)