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Year 11
Higher

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
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Year 11
Higher

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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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.
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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
tick

values less than 3

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

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

Correct Answer:$$x\ge3$$,values greater than or equal to 3
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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 $$y=3x-2$$
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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 $$y=\frac{1}{2}x+3$$
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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
tick

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 $$y=\frac{1}{2}x+3$$
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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 $$y<2-x$$
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$$y>2x+5$$ and $$y<2-x$$

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

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

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

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

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

$$y<2x+5$$ 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)