Pass Functional Skills logo

Simultaneous equations

Simultaneous equations for A Level Politics AQA: what it means, how to set the working out, and the questions it is asked in.
  • A Level
  • AQA
  • Politics
  • Spec S7 · S9
  • 4 min read
  • 6 revision boxes

Introduction

2 boxes
1 min read

What is simultaneous equations?

Listen to this box

Transcript

A short spoken summary of simultaneous equations and where it is used.

A spoken walk-through of simultaneous equations before you read the notes.
Sketch the shape even when the question does not ask for one — it makes the next step obvious.
5 rows

The simultaneous equations reference table

Practise the routine version until it is automatic, then move to the multi-step questions.
The layout below is the one the mark scheme expects.

Diagram showing simultaneous equations laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.
Term
Meaning
Example
Row 1 column 1
Row 1 column 2
×10\times 10 moves every digit one column left
Row 2 column 1
Row 2 column 2
×10\times 10 moves every digit one column left
Row 3 column 1
Row 3 column 2
≈160\approx 160

Learning

2 boxes
3 steps

How to work with simultaneous equations

The examiner marks the working, so a correct answer with no method still drops marks.
  1. Read the question and write down what is being asked for.
  2. Set out the working for simultaneous equations in the order the method gives.
  3. Substitute the values and simplify.
  4. Check the answer against an estimate before writing it down.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: 49=7\sqrt{49} = 7.
Answer: 49=7\sqrt{49} = 7
3 rules

Key facts: Simultaneous equations

This idea appears again in the higher-mark questions, so it is worth over-learning.
The layout below is the one the mark scheme expects.

Diagram showing simultaneous equations laid out step by step

The same idea drawn out, so the method is visible.

  • Rule 1

    How simultaneous equations behaves in the 1st of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0

  • Rule 2

    How simultaneous equations behaves in the 2nd of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 3

    How simultaneous equations behaves in the 3rd of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

20 minutes

Get your predicted grade

Twenty questions gives you a predicted grade, your target, and the gap between them — plus the topics that close it fastest.
Get my predicted grade

Examples

2 boxes
3 marks · worked

Worked example: simultaneous equations

This idea appears again in the higher-mark questions, so it is worth over-learning.
4 marks · worked

Practice question 6: 49=7\sqrt{49} = 7

Practise the routine version until it is automatic, then move to the multi-step questions.
The layout below is the one the mark scheme expects.

Diagram showing simultaneous equations laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: x2+5x+6=0x^2 + 5x + 6 = 0.

Practice bank

Thousands of revision questions

Every topic is backed by graded practice with instant marking and full solutions.
Try it now
Practice questions
7,000+
Topics
10
Marking and solutions
Instant

Common questions

How many marks is simultaneous equations usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the A Level Politics AQA paper?
Yes — it sits in the Vectors strand.