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Simultaneous equations

Simultaneous equations for GCSE Business Studies AQA: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • AQA
  • Business Studies
  • Spec A8 · A20 · A1
  • 9 min read
  • 9 revision boxes

Introduction

2 boxes
4 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.
The specification wording is precise here, and the mark scheme follows that wording exactly.
Worth knowing: ×10\times 10 moves every digit one column left.
5 rows

The simultaneous equations reference table

Read the units in the question before you start; a converted unit is the most common slip.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.
Term
Meaning
Example
Common slip
Row 1 column 1
Row 1 column 2
x2+5x+6=0x^2 + 5x + 6 = 0
Row 1 column 4
Row 2 column 1
Row 2 column 2
x2+5x+6=0x^2 + 5x + 6 = 0
Row 2 column 4

Learning

5 boxes
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.
  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: ≈160\approx 160.
Answer: 34×25\frac{3}{4} \times \frac{2}{5}
2 rules

Key facts: Simultaneous equations

Work through the method one line at a time and write down what changes at each step.
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: 34×25\frac{3}{4} \times \frac{2}{5}.

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

Key facts: Simultaneous equations

Read the units in the question before you start; a converted unit is the most common slip.
Worth knowing: 34×25\frac{3}{4} \times \frac{2}{5}.

  • Rule 1

    How simultaneous equations behaves in the 1st of the cases the specification names.
    ≈160\approx 160

  • 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.
    ×10\times 10 moves every digit one column left
5 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.
  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: a2+b2=c2a^2 + b^2 = c^2

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Examples

2 boxes
1 marks · worked

Worked example: simultaneous equations

Read the units in the question before you start; a converted unit is the most common slip.
3 marks · worked

Practice question 9: ≈160\approx 160

The examiner marks the working, so a correct answer with no method still drops marks.
Worth knowing: ×10\times 10 moves every digit one column left.

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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 Business Studies AQA paper?
Yes — it sits in the Vectors strand.