Choose exam board for KS4 Computer Science (GCSE)
Choose exam board for KS4 English
Choose exam board for KS4 French
Choose exam board for KS4 Geography
Choose exam board for KS4 German
Choose exam board for KS4 History
Choose tier for KS4 Maths
Choose exam board for KS4 Music
Choose exam board for KS4 Physical education (GCSE)
Choose exam board for KS4 Religious education (GCSE)
Choose exam board for KS4 Spanish

Solving algebraic simultaneous equations by elimination

Lesson details

Learning outcome

I can solve two linear simultaneous equations algebraically using elimination.

Key learning points

  1. It is possible to find a solution that satisfies two equations with two unknowns by trial and error.
  2. A more efficient method is to combine the two equations to create a third valid equation .
  3. If the third equation contains only one unknown, it is easy to solve .
  4. 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

Performing different operations on different variables. E.g. subtracting one variable to eliminate then adding the other variable and constant. Pupils incorrectly think they are adding to eliminate.

This is caused by negative number skills. Subtracting two identical values always gives zero even if both are negative. If a term is the same in both equations, we subtract to eliminate. Clear working is crucial here.

Teacher tip

Pupils should be checking their answers satisfy both equations at every opportunity.

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

Loading...

Prior knowledge starter quiz

6 Questions

Q1.
If ◉ ◉ ◯ = 14 points and ◉◉ ◯ ◯ = 16 points, what is the value of ◉?

Correct Answer: 6, 6 points

Q2.
If ◉◉◯ = 15 points and ◉◯◯ = 12 points, what is the value of ◉?

Correct Answer: 6

Q3.
Given that ◉◉◯◯ = 20 points and ◯◯◯◉ = 22 points, what is the value of ◉?

Correct Answer: 4

Q4.
Assuming ◉◯ = 9 points and ◉◉◯◯◯ = 25 points, what is the value of ◉?

Correct Answer: 2

Q5.
Which equation is true for $$x = 5$$ and $$y = 1$$?

$$2x + y = -8$$
Correct answer: $$2x + y = 11$$
$$2x + y = 4$$

Q6.
When ◉◉◯◯◯ = 28 points and ◉◉◉◯ = 28 points, what is the value of ◉?

Correct Answer: 8

6 Questions

Q1.
Multiply this equation by $$4$$: $$3x + 10 = 40$$

Correct Answer: 12x + 40 = 160

Q2.
Multiply this equation by $$3$$: $$20 + 2y = 16$$

Correct Answer: 60 + 6y = 48, 6y + 60 = 48

Q3.
Multiply this equation by $$4$$: $$5x + 10y = 100$$

$$20x + 10y = 400$$
$$9x + 14y = 104$$
Correct answer: $$20x + 40y = 400$$

Q4.
Which of these steps would match the y coefficients for equations 1) $$3x + 4y = 45$$ and 2) $$5x + 8y = 83$$:

Correct answer: double equation 1
add both equations together
double equation 2

Q5.
What is the value of x for $$4x + 4y = 28$$ and $$3x + 8y = 36$$ ?

Correct answer: $$x = 4, y = 3$$
$$x = 5, y = 2$$
$$x = 3, y = 4$$

Q6.
What is the value of x for equations $$3x + 4y = 33$$ and $$x + 3y = 16$$ ?

Correct Answer: 7, x = 7

To help you plan your 10 maths lesson on: Solving algebraic simultaneous equations by elimination, download all teaching resources for free and adapt to suit your pupils' needs...