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- Year 10•
- Foundation
Solving more complex simultaneous equations by elimination
I can solve two complex linear simultaneous equations algebraically using elimination.
- Year 10•
- Foundation
Solving more complex simultaneous equations by elimination
I can solve two complex linear simultaneous equations algebraically using elimination.
Lesson details
Key learning points
- Additively combining the equations does not eliminate one variable unless the coefficients are the same.
- Equivalent equations should be formed so the coefficients of one variable are the same (if not already).
- When considering the coefficients, use your knowledge of LCM to help.
Keywords
Simultaneous equations - Equations which represent different relationships between the same variables are called simultaneous equations.
Elimination - Elimination is a technique to help solve equations simultaneously and is where one of the variables in a problem is removed.
Common misconception
Forgetting to multiply every term in the equation when scaling or not multiplying every term by the same value.
Remind pupils that in order to maintain equality, the entire expression on both sides of the equals sign must be multiplied by the same value. Clear working and checking solutions can help pupils spot when they have made this mistake.
To help you plan your year 10 maths lesson on: Solving more complex simultaneous equations by elimination, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 10 maths lesson on: Solving more complex simultaneous equations by elimination, 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.Which equation is true for $$x = 3$$ and $$y = -2$$?
Q2.If I add together the pair of simultaneous equations $$4x + ay = 12$$ and $$5x - ay = 26$$, what is the resulting equation?
Q3.Which equation is true for $$x = \frac{1}{2}$$ and $$y = 2$$?
Q4.If I add together the pair of simultaneous equations $$x + y = 28$$ and $$x - y = 12$$, what is the resulting equation?
Q5.Which equation is true for $$x = -5$$ and $$y = -2$$?
Q6.If I add together the pair of simultaneous equations $$2x - 3y = 30$$ and $$y -2x = 6$$, what is the resulting equation?
Assessment exit quiz
6 Questions
Q1.Which multiplier would match the y coefficients for equations 1) $$15x + 4y = 12$$ and 2) $$2x + 2y = 6$$:
Q2.Which multiplier would match the x coefficients for equations 1) $$3x + 5y = 21$$ and 2) $$x + 2y = 8$$:
Q3.Which multiplier would match coefficients for either $$x$$ or $$y$$ for equations 1) $$5x + 4y = -13$$ and 2) $$10x + 2y = -44$$:
Q4.What is the value of $$y$$ for simultaneous equations $$x + 4y = 7$$ and $$2x + 3y = -1$$
Q5.What is the value of $$y$$ for simultaneous equations $$3x + 4y = 10$$ and $$2x + 2y = 4$$
Q6.What is the value of $$x$$ for simultaneous equations $$3x + 3y = 21$$ and $$2x + y = 9$$