Myths about teaching can hold you back
- Year 10•
- Foundation
Solving simultaneous linear equations graphically
I can solve two linear simultaneous equations graphically (0 or 1 or infinitely many solutions).
- Year 10•
- Foundation
Solving simultaneous linear equations graphically
I can solve two linear simultaneous equations graphically (0 or 1 or infinitely many solutions).
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.
To help you plan your year 10 maths lesson on: Solving simultaneous linear equations graphically, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 10 maths lesson on: Solving simultaneous linear equations graphically, 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 Simultaneous equations: 2 variables unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Lesson video
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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?