New
New
Year 10
Higher

Solving simultaneous equations via any method

I can determine which method of solving is most appropriate and interpret the solutions (in context).

Link copied to clipboard

New
New
Year 10
Higher

Solving simultaneous equations via any method

I can determine which method of solving is most appropriate and interpret the solutions (in context).

Link copied to clipboard

These resources will be removed by end of Summer Term 2025.

Switch to our new teaching resources now - designed by teachers and leading subject experts, and tested in classrooms.

These resources were created for remote use during the pandemic and are not designed for classroom teaching.

Lesson details

Key learning points

  1. The features of the equations may mean one method is more preferable for solving.
  2. You can use any of the methods that are valid.
  3. You can use the other methods to check your solution.
  4. The solution should be interpreted in context if context was stated.

Keywords

  • Substitution - Substitute means to put in place of another. In algebra, substitution can be used to replace variables with values, terms, or expressions.

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

Common misconception

One method is superior when solving simultaneous equations.

Understanding that there are often multiple ways to solve the same problem and then be able to accurately execute a variety of methods is very useful. In this topic, it can enable pupils to confirm their solutions.


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

A good challenge is to ask pupils to solve the same pair of linear equations using three or more methods. This is an opportunity for them to practice their fluency and also to acknowledge that they have the capacity to check and confirm their own answers.
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

6 Questions

Q1.
Using substitution, what is the value of x for simultaneous equations 6x+4y=32 and 3x+9y=51?
Correct Answer: 2, x = 2
Q2.
Using substitution, what is the value of x for simultaneous equations 7x+2y=36 and 4x+2y=30?
Correct Answer: 2, x = 2
Q3.
Using substitution, what is the value of y for simultaneous equations yx=1 and 3x+y=19?
Correct Answer: 4, y = 4
Q4.
Which multiplier would match the x coefficients for equations 1) 6x+10y=42 and 2) x+2y=8:
multiply equation 1) by 2
multiply equation 1) by 3
Correct answer: multiply equation 2) by 6
multiply equation 2) by 5
Q5.
What is the value of y for simultaneous equations x+4y=7 and 2x+3y=1
Correct Answer: 3, y = 3
Q6.
What is the value of x for simultaneous equations x+y=7 and 6x+3y=27
Correct Answer: 2, x = 2

6 Questions

Q1.
Solve using any method: 3x+5y=6 and 5x5y=30. Write your answer in the form (x,y).
Correct Answer: (3, -3)
Q2.
Solve using any method: 3x+y=15 and 5x5y=45. Write your answer in the form (x,y).
Correct Answer: (6, -3)
Q3.
Solve using any method: 6x+2y=30 and 6x5y=51. Write your answer in the form (x,y).
Correct Answer: (6, -3)
Q4.
Solve using any method: 8x+2y=10 and 3x4y=18. Write your answer in the form (x,y).
Correct Answer: (2, -3)
Q5.
Solve using any method: x+5y=24 and 5x+3y=10. Write your answer in the form (x,y).
Correct Answer: (-1, 5)
Q6.
Solve using any method: 5x+4y=11 and 2x+5y=35. Write your answer in the form (x,y).
Correct Answer: (-5, 9)
This site uses cookies to store information on your computer. Some of these cookies are essential, while others help us to improve your experience by providing insights into how the site is being used.