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Year 10
Higher

Combining equations

I can additively combine two equations to create a third valid equation.

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New
New
Year 10
Higher

Combining equations

I can additively combine two equations to create a third valid equation.

Download all resources
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Share activities with pupils
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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. Two equations can be combined into a third equation.
  2. You can combine equations using the standard arithmetic operations.
  3. The new equation may not contain both variables any more.

Keywords

  • Elimination - Elimination is a technique to help solve equations simultaneously and is where one of the variables in a problem is removed.

Common misconception

Mistakes can be made when subtracting negative values. E.g. thinking that 5 - - 2 = 3.

Consider additive inverses, subtracting a negative is the same as adding the additive inverse. Pupils should be able to spot mistakes in learning cycle 1 by checking their new equation is still true.


To help you plan your year 10 maths lesson on: Combining equations, download all teaching resources for free and adapt to suit your pupils' needs...

Pupils should get used to labelling their equations so they can make it clear which equations they are manipulating and what operations they are performing when they are writing their solutions.
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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.
Which pair of coordinates does not satisfy the equation $$y = 2x + 4$$?
(1, 6)
(2, 8)
(3, 10)
Correct answer: (4, 11)
Q2.
The area of a rectangle is $$90 cm^2$$. The perimeter is $$94 cm$$. Which two equations are true for side lengths $$a$$ and $$b$$?
Correct answer: $$ab = 90$$
$$a + b = 94$$
Correct answer: $$2(a + b) = 94$$
$$ab = 94$$
Q3.
Which two of the following are correct for a right triangle with sides $$a, b$$ and hypotenuse $$c$$?
$$a + b + c = abc$$
Correct answer: $$Area = \frac{ab}{2}$$
Correct answer: $$Perimeter = a + b + c$$
$$Area = ab$$
Q4.
If $$x = -9$$, what is the value of $$y$$ for $$x + 2y = 13$$?
Correct Answer: 11, y=11
Q5.
Which pair of coordinates does not satisfy the equation $$y = -3x + 2$$?
(-1, 5)
(0, 2)
Correct answer: (1, 1)
(2, -4)
Q6.
There are 12 goals scored in a football match. Team A scored $$a$$ goals, and winning Team B scored $$b$$ goals. The winning team scored 5 more than the losing team.
Correct answer: $$a + b = 12$$
$$a + b = 5$$
$$a = b - 5$$
Correct answer: $$a = b - 5$$

Exit quiz

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6 Questions

Q1.
Which equation is true for $$x = 2$$ and $$y = 5$$?
$$2x + y = -8$$
Correct answer: $$2x + 3y = 19$$
$$4x + 2y = 20$$
Q2.
Which equation is true for $$x = 3$$ and $$y = 9$$?
$$2x + 3y = 12$$
$$3x + y = 16$$
Correct answer: $$2(x + y) = 24$$
Q3.
Which equation is true for $$x = -2$$ and $$y = 3$$?
Correct answer: $$3y - x = 11$$
$$3y - x = 7$$
$$3x - y = 9$$
Q4.
Which equation is true for $$x = 8$$ and $$y = 1$$?
$$x^2 - y^2 = 64$$
$$x^2 = 34y$$
Correct answer: $$x^2 + y = 65$$
Q5.
If I add together the pair of simultaneous equations $$5x + 7y = 87$$ and $$7x + 7y = 91$$, what is the resulting equation?
Correct Answer: 12x + 14y = 178
Q6.
If I add together the pair of simultaneous equations $$5x + 2y = 10$$ and $$7x - 2y = -50$$, what is the resulting equation?
Correct Answer: 12x = -40