PAss Functional Skills

Solving linear equations

Solving linear equations for Functional Skills Environmental Science: what it means, how to set the working out, and the questions it is asked in.
  • Functional Skills
  • Environmental Science
  • Spec G17 · G6 · G8
  • 9 min read
  • 9 revision boxes

Introduction

2 boxes
4 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.
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.
Worth knowing: x2+5x+6=0x^2 + 5x + 6 = 0.
6 rows

The solving linear equations reference table

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: ≈160\approx 160.
Term
Meaning
Example
Row 1 column 1
Row 1 column 2
34×25\frac{3}{4} \times \frac{2}{5}
Row 2 column 1
Row 2 column 2
≈160\approx 160
Row 3 column 1
Row 3 column 2
34×25\frac{3}{4} \times \frac{2}{5}
Row 4 column 1
Row 4 column 2
a2+b2=c2a^2 + b^2 = c^2

Learning

5 boxes
4 steps

How to work with solving linear equations

Read the units in the question before you start; a converted unit is the most common slip.
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: a2+b2=c2a^2 + b^2 = c^2.
Answer: a2+b2=c2a^2 + b^2 = c^2
2 rules

Key facts: Solving linear equations

The specification wording is precise here, and the mark scheme follows that wording exactly.

  • 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.
    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
3 steps

How to work with solving linear equations

Work through the method one line at a time and write down what changes at each step.
  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: x2+5x+6=0x^2 + 5x + 6 = 0
3 rules

Key facts: Solving linear equations

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

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

How to work with solving linear equations

Read the units in the question before you start; a converted unit is the most common slip.
  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: a2+b2=c2a^2 + b^2 = c^2

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Examples

2 boxes
1 marks · worked

Worked example: 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.
Worth knowing: ×10\times 10 moves every digit one column left.
1 marks · worked

Practice question 9: a2+b2=c2a^2 + b^2 = c^2

This idea appears again in the higher-mark questions, so it is worth over-learning.
Worth knowing: ×10\times 10 moves every digit one column left.

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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 Environmental Science paper?
Yes — it sits in the Trigonometry strand.