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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.
- 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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Lesson details
Key learning points
- If a point on neither line is substituted into the equations, neither equation will be valid
- If a point on one of the lines is substituted into the equations, one equation will be valid
- Depending on the location of the point, the equation may evaluate to a bigger or smaller value
- 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...
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.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 4 maths lessons from the Inequalities unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
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Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.Match up the inequalities to the statements.
$$x<3$$ -
values less than 3
$$x\le3$$ -
values less than or equal to 3
$$x>3$$ -
values greater than 3
$$x\ge3$$ -
values greater than or equal to 3
Q2.Which of these are valid inequalities?
Q3.Which of these solutions satisfy the equation $$y=3x-1$$?
Q4.Which of these coordinates are on the line with equation $$y=2x+5$$?
Q5.Using the graph or otherwise, what is the solution to the equations $$y=2x+5$$ and $$y=2-x$$ simultaneously?
Q6.Which of these equations is $$x=5, y=3$$ a solution to?
Assessment exit quiz
6 Questions
Q1.Which of these coordinates satisfy the inequality $$y>2x$$?
Q2.Using the graph of $$y=5-2x$$ (or otherwise) which coordinates satisfy the inequality $$y<5-2x$$?
Q3.Match the solutions to the descriptions. Use the graphs to help you.
$$x=-2, y=2$$ -
Solution to $$y=\frac{1}{2}x+3$$ but not a solution to $$y=3x-2$$
$$x=1, y=1$$ -
Solution to $$y=3x-2$$ but not a solution to $$y=\frac{1}{2}x+3$$
$$x=2, y=4$$ -
Solution to both $$y=3x-2$$ and $$y=\frac{1}{2}x+3$$ simultaneously
$$x=5, y=5$$ -
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)?
Q5.Match the coordinates to the correct statements.
(-3, 3) -
$$y>2x+5$$ and $$y<2-x$$
(-2, 4) -
$$y>2x+5$$ and $$y=2-x$$
(-1, 2) -
$$y<2x+5$$ and $$y<2-x$$
(0, 5) -
$$y=2x+5$$ and $$y>2-x$$
(1, 1) -
$$y<2x+5$$ and $$y=2-x$$
(2, 2) -
$$y<2x+5$$ and $$y>2-x$$
Q6.Which coordinate pair satisfies the inequalities $$y>x-1$$ and $$y<2x-1$$?
