PAss Functional Skills

Solving linear equations

Solving linear equations for GCSE Law OCR Higher: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • OCR
  • Law
  • Higher
  • Spec P7 · P19 · P18
  • 11 min read
  • 9 revision boxes

Introduction

2 boxes
1 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.
Check the answer against an estimate before you move on, so a place-value slip is caught here.
5 rows

The solving linear equations reference table

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.
Term
Meaning
Example
Common slip
Row 1 column 1
Row 1 column 2
49=7\sqrt{49} = 7
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
≈160\approx 160
Row 3 column 4
Row 4 column 1
Row 4 column 2
≈160\approx 160
Row 4 column 4

Learning

5 boxes
3 steps

How to work with solving linear 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 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.
  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: 49=7\sqrt{49} = 7
3 rules

Key facts: Solving linear 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 solving linear equations laid out step by step

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

  • Rule 1

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

  • 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}

  • Rule 3

    How solving linear 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 solving linear equations

Check the answer against an estimate before you move on, so a place-value slip is caught here.
Worth knowing: x2+5x+6=0x^2 + 5x + 6 = 0.
  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: ≈160\approx 160
2 rules

Key facts: Solving linear equations

Work through the method one line at a time and write down what changes at each step.

  • Rule 1

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

  • 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.
    x2+5x+6=0x^2 + 5x + 6 = 0
4 steps

How to work with solving linear equations

The specification wording is precise here, and the mark scheme follows that wording exactly.
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 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: x2+5x+6=0x^2 + 5x + 6 = 0.
Answer: x2+5x+6=0x^2 + 5x + 6 = 0

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
4 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: x2+5x+6=0x^2 + 5x + 6 = 0.
1 marks · worked

Practice question 9: ×10\times 10 moves every digit one column left

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

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 GCSE Law OCR Higher paper?
Yes — it sits in the Trigonometry strand.