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Simultaneous equations

Simultaneous equations for GCSE French Edexcel: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • Edexcel
  • French
  • Spec R16 · R19
  • 10 min read
  • 9 revision boxes

Introduction

2 boxes
4 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.
Practise the routine version until it is automatic, then move to the multi-step questions.
Worth knowing: ×10\times 10 moves every digit one column left.
5 rows

The simultaneous equations reference table

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
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.
Term
Meaning
Example
Common slip
Row 1 column 1
Row 1 column 2
34×25\frac{3}{4} \times \frac{2}{5}
Row 1 column 4
Row 2 column 1
Row 2 column 2
a2+b2=c2a^2 + b^2 = c^2
Row 2 column 4
Row 3 column 1
Row 3 column 2
x2+5x+6=0x^2 + 5x + 6 = 0
Row 3 column 4
Row 4 column 1
Row 4 column 2
×10\times 10 moves every digit one column left
Row 4 column 4

Learning

5 boxes
4 steps

How to work with 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.
  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: 34×25\frac{3}{4} \times \frac{2}{5}.
Answer: a2+b2=c2a^2 + b^2 = c^2
2 rules

Key facts: Simultaneous equations

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

  • Rule 1

    How simultaneous equations behaves in the 1st of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 2

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

  • Rule 3

    How simultaneous equations behaves in the 3rd of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0
4 steps

How to work with simultaneous equations

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: 49=7\sqrt{49} = 7.
  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: ×10\times 10 moves every digit one column left.
Answer: ≈160\approx 160
3 rules

Key facts: Simultaneous equations

Sketch the shape even when the question does not ask for one — it makes the next step obvious.

  • Rule 1

    How simultaneous equations behaves in the 1st of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}

  • Rule 2

    How simultaneous equations behaves in the 2nd of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}

  • Rule 3

    How simultaneous equations behaves in the 3rd of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0
5 steps

How to work with simultaneous equations

This idea appears again in the higher-mark questions, so it is worth over-learning.
Worth knowing: 49=7\sqrt{49} = 7.
  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: 34×25\frac{3}{4} \times \frac{2}{5}.
Answer: x2+5x+6=0x^2 + 5x + 6 = 0

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Examples

2 boxes
1 marks · worked

Worked example: simultaneous equations

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
Worth knowing: 49=7\sqrt{49} = 7.
4 marks · worked

Practice question 9: 34×25\frac{3}{4} \times \frac{2}{5}

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 French Edexcel paper?
Yes — it sits in the Vectors strand.