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Solving linear equations

Solving linear equations for Functional Skills Music: what it means, how to set the working out, and the questions it is asked in.
  • Functional Skills
  • Music
  • Spec N19
  • 10 min read
  • 10 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.
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: ×10\times 10 moves every digit one column left.
3 rows

The solving linear equations reference table

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}.
Term
Meaning
Example
Row 1 column 1
Row 1 column 2
×10\times 10 moves every digit one column left
Row 2 column 1
Row 2 column 2
a2+b2=c2a^2 + b^2 = c^2
Row 3 column 1
Row 3 column 2
×10\times 10 moves every digit one column left

Learning

6 boxes
3 steps

How to work with solving linear equations

Practise the routine version until it is automatic, then move to the multi-step questions.
  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
3 rules

Key facts: 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.

  • Rule 1

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

  • 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}
4 steps

How to work with solving linear 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 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: 34×25\frac{3}{4} \times \frac{2}{5}.
Answer: x2+5x+6=0x^2 + 5x + 6 = 0
2 rules

Key facts: Solving linear equations

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

  • Rule 1

    How solving linear equations behaves in the 1st of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0

  • Rule 2

    How solving linear equations behaves in the 2nd of the cases the specification names.
    ×10\times 10 moves every digit one column left

  • Rule 3

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

How to work with solving linear 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 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: 34×25\frac{3}{4} \times \frac{2}{5}.
Answer: ×10\times 10 moves every digit one column left
3 rules

Key facts: Solving linear equations

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
Worth knowing: ≈160\approx 160.

  • 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.
    ×10\times 10 moves every digit one column left

  • Rule 3

    How solving linear equations behaves in the 3rd of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

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Examples

2 boxes
3 marks · worked

Worked example: 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.
2 marks · worked

Practice question 10: x2+5x+6=0x^2 + 5x + 6 = 0

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.

Practice bank

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Topics
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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 Functional Skills Music paper?
Yes — it sits in the Trigonometry strand.