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Solving linear equations

Solving linear equations for ESOL Statistics: what it means, how to set the working out, and the questions it is asked in.
  • ESOL
  • Statistics
  • Spec G4
  • 8 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.
The specification wording is precise here, and the mark scheme follows that wording exactly.
4 rows

The solving linear equations reference table

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}.
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
34×25\frac{3}{4} \times \frac{2}{5}
Row 2 column 4

Learning

6 boxes
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.
  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: 34×25\frac{3}{4} \times \frac{2}{5}
3 rules

Key facts: Solving linear equations

Work through the method one line at a time and write down what changes at each step.
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.
    ×10\times 10 moves every digit one column left

  • 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.
    a2+b2=c2a^2 + b^2 = c^2
5 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: ≈160\approx 160.
Answer: 49=7\sqrt{49} = 7
2 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.
    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}

  • 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}
3 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.
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.
  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: 34×25\frac{3}{4} \times \frac{2}{5}
3 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.
    ×10\times 10 moves every digit one column left

  • Rule 2

    How solving linear equations behaves in the 2nd of the cases the specification names.
    49=7\sqrt{49} = 7

  • Rule 3

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

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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.
3 marks · worked

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

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

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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 ESOL Statistics paper?
Yes — it sits in the Trigonometry strand.