PAss Functional Skills

Simultaneous equations

Simultaneous equations for GCSE History AQA: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • AQA
  • History
  • Spec S16 · S7 · S12
  • 7 min read
  • 7 revision boxes

Introduction

2 boxes
2 min read

What is simultaneous equations?

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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.
Check the answer against an estimate before you move on, so a place-value slip is caught here.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.
5 rows

The simultaneous equations reference table

Work through the method one line at a time and write down what changes at each step.
Term
Meaning
Example
Common slip
Marks
Row 1 column 1
Row 1 column 2
34×25\frac{3}{4} \times \frac{2}{5}
Row 1 column 4
Row 1 column 5
Row 2 column 1
Row 2 column 2
×10\times 10 moves every digit one column left
Row 2 column 4
Row 2 column 5
Row 3 column 1
Row 3 column 2
a2+b2=c2a^2 + b^2 = c^2
Row 3 column 4
Row 3 column 5

Learning

3 boxes
4 steps

How to work with simultaneous equations

The specification wording is precise here, and the mark scheme follows that wording exactly.
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: ≈160\approx 160.
  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.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: a2+b2=c2a^2 + b^2 = c^2.
Answer: ×10\times 10 moves every digit one column left
2 rules

Key facts: Simultaneous equations

Read the units in the question before you start; a converted unit is the most common slip.
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.
    x2+5x+6=0x^2 + 5x + 6 = 0
4 steps

How to work with simultaneous equations

Check the answer against an estimate before you move on, so a place-value slip is caught here.
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: ≈160\approx 160.
  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: x2+5x+6=0x^2 + 5x + 6 = 0.
Answer: 49=7\sqrt{49} = 7

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Examples

2 boxes
4 marks · worked

Worked example: simultaneous equations

Work through the method one line at a time and write down what changes at each step.
Worth knowing: x2+5x+6=0x^2 + 5x + 6 = 0.
3 marks · worked

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

The examiner marks the working, so a correct answer with no method still drops marks.

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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 GCSE History AQA paper?
Yes — it sits in the Vectors strand.