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Solving simultaneous equations by elimination from a context

I can solve two linear simultaneous equations given in context using elimination.

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Solving simultaneous equations by elimination from a context

I can solve two linear simultaneous equations given in context using elimination.

Lesson details

Key learning points

  1. It is possible to find a solution that satisfies a problem with two unknowns by trial and error.
  2. It is possible to use the difference between the two scenarios to create a third valid scenario.
  3. Once you know one of the unknowns, you can substitute to find the other.

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

Subtracting the variables one way round but the constants the other way.

Pupils could rewrite their equations so the one they are subtracting is underneath in a column method. For this lesson, the answers are in context so pupils should spot when negative answers do not make sense.

This is a good time to re-enforce the importance of checking answers. Pupils should be checking their values work for both pieces of information. They could use a calculator here to help.
Teacher tip

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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Prior knowledge starter quiz

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6 Questions

Q1.
Which equation is true for $$x = 4$$ and $$y = 5$$?

$$2x + y = 9$$
Correct answer: $$2x + 3y = 23$$
$$4x + y = 20$$

Q2.
If I add together the pair of simultaneous equations $$9x + 3y = 10$$ and $$6x + y = 30$$, what is the resulting equation?

Correct Answer: 15x + 4y = 40

Q3.
Which equation is true for $$x = 4$$ and $$y = 6$$?

Correct answer: $$3x + 2y = 24$$
$$3x + y = 20$$
$$x + 2y = 14$$

Q4.
If I add together the pair of simultaneous equations $$3x + 2y = 10$$ and $$3y - 3x = 40$$, what is the resulting equation?

Correct Answer: 5y = 50

Q5.
Which equation is true for $$x = -2$$ and $$y = 5$$?

$$3x + 2y = 6$$
Correct answer: $$3x + 2y = 4$$
$$3x + 2y = 11$$

Q6.
If I add together the pair of simultaneous equations $$13x + 2y = 10$$ and $$7x - 2y = 40$$, what is the resulting equation?

Correct Answer: 20x = 50

Assessment exit quiz

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6 Questions

Q1.
If ◉ ◉ ◯ = 25 points and ◉ ◉ ◯ ◯ = 30 points, what is the value of ◉?

Correct Answer: 10, 10 points

Q2.
If ◉ ◉ ◯ ◯ = 18 points and ◉ ◯ ◯ = 11 points, what is the value of ◉?

Correct Answer: 7, 7 points

Q3.
If ◉ ◉ ◯ ◯ = 20 points and ◉ ◯ ◯ = 12 points, what is the value of ◯?

Correct Answer: 2, 2 points

Q4.
If ◉ ◉ ◯ = 23 points and ◉ - (◯) = 10 points, what is the value of ◯?

Correct Answer: 1, 1 point

Q5.
If ◉ ◉ ◯ = 17 points and ◉ - (◯) = 10 points, what is the value of ◯?

Correct Answer: -1, -1 point

Q6.
If ◉ ◉ ◉ ◯ = 33 points and ◉ ◉ ◉ ◯ ◯ = 36 points, what is the value of ◉?

Correct Answer: 10, 10 points

Lesson appears in

UnitMaths / Simultaneous equations: 2 variables

Maths

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