Pass Functional Skills logo

Solving linear equations

Solving linear equations for A Level Business Studies OCR: what it means, how to set the working out, and the questions it is asked in.
  • A Level
  • OCR
  • Business Studies
  • Spec P14
  • 9 min read
  • 8 revision boxes

Introduction

2 boxes
3 min read

What is solving linear equations?

Listen to this box

Transcript

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

A spoken walk-through of solving linear equations before you read the notes.
The examiner marks the working, so a correct answer with no method still drops marks.
Worth knowing: 34×25\frac{3}{4} \times \frac{2}{5}.
4 rows

The solving linear equations reference table

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 solving linear equations laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: 49=7\sqrt{49} = 7.
Term
Meaning
Example
Common slip
Row 1 column 1
Row 1 column 2
≈160\approx 160
Row 1 column 4
Row 2 column 1
Row 2 column 2
×10\times 10 moves every digit one column left
Row 2 column 4
Row 3 column 1
Row 3 column 2
34×25\frac{3}{4} \times \frac{2}{5}
Row 3 column 4
Row 4 column 1
Row 4 column 2
34×25\frac{3}{4} \times \frac{2}{5}
Row 4 column 4

Learning

4 boxes
3 steps

How to work with solving linear equations

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.
  1. Read the question and write down what is being asked for.
  2. Set out the working for solving linear 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: a2+b2=c2a^2 + b^2 = c^2
3 rules

Key facts: Solving linear equations

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.

  • Rule 1

    How solving linear equations behaves in the 1st of the cases the specification names.
    49=7\sqrt{49} = 7

  • Rule 2

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

  • Rule 3

    How solving linear equations behaves in the 3rd of the cases the specification names.
    49=7\sqrt{49} = 7
4 steps

How to work with solving linear equations

The examiner marks the working, so a correct answer with no method still drops marks.
The layout below is the one the mark scheme expects.

Diagram showing solving linear 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 solving linear 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: ≈160\approx 160.
Answer: x2+5x+6=0x^2 + 5x + 6 = 0
2 rules

Key facts: Solving linear equations

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

  • Rule 1

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

  • Rule 2

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

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
2 marks · worked

Worked example: solving linear equations

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
Worth knowing: ×10\times 10 moves every digit one column left.
4 marks · worked

Practice question 8: ≈160\approx 160

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 solving linear equations laid out step by step

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

Practice bank

Thousands of revision questions

Every topic is backed by graded practice with instant marking and full solutions.
Try it now
Practice questions
5,000+
Topics
10
Marking and solutions
Instant

Common questions

How many marks is solving linear equations usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the A Level Business Studies OCR paper?
Yes — it sits in the Trigonometry strand.