Skip to main content
MathidiaMathematics Academy
Simultaneous equations
Lesson 26 of 75
Introduction

Graphical solutions

Objective. Interpret the intersection of two lines as a shared solution.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Graphical solutions develops a connected mathematical idea rather than an isolated trick. Find values satisfying two linear relationships at once. Begin by representing the quantities or relationships, choose a rule that fits, justify each transformation, and finish by checking units, signs, scale and whether the answer is reasonable.

Worked example

Tickets cost £2 for children and £5 for adults. Write an equation for 3 children and 4 adults.

£2.00
Money illustration for £2
  1. 1Identify the known information, the unknown and any conditions.
  2. 2Choose a diagram, table, graph or algebraic representation that exposes the structure.
  3. 3Apply the relevant rule one justified step at a time, keeping exact values where useful.
  4. 4Check by substitution, inverse reasoning or estimation. The result is 2c + 5a = 26.

Answer: 2c + 5a = 26

Concept mastery

Based on your past attempts at this lesson — the question types to practise again come first.

Complete a practice set to see your concept breakdown here.

Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

Start practising

Common mistake. A common error in graphical solutions is to copy a procedure without checking its conditions. Label the structure first and justify every sign, operation and unit.

Your progress

Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.

0 of 5 steps complete

Your place saves automatically as you read.

My dashboard