A-Level Maths Simultaneous Equations and Inequalities

Everything you need to know about simultaneous equations and inequalities for A-Level Maths. Save countless hours of time!

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Simultaneous Equations and Inequalities Topics for A-Level Maths

This module will teach you the following:

Year 1

  • Simultaneous equations: Solving by substitution and solving by elimination
    • Solving two linear equations simultaneously
    • Solving a linear equation and a quadratic equation simultaneously.
  • Inequalities: linear and quadratic

What’s Included?

We’ve created 52 modules covering every Maths topic needed for A level, and each module contains:

  • An editable PowerPoint lesson presentation
  • Editable revision handouts
  • A glossary which covers the key terminologies of the module
  • Topical mind maps for visualising the key concepts
  • Printable flashcards to help students engage active recall and confidence-based repetition
  • A quiz with accompanying answer key to test knowledge and understanding of the module

As a premium member, once rolled out you get access to the entire library of A-Level Maths resources. For now, we have made the first five topics completely free of charge for you to get a taste of what’s to come.

A Level Maths Resources Mapped by Exam Board

Once completed our modules can be used with both UK and international A Level examination board specifications.

We will put together comprehensive mapping documents which will show you exactly which modules align to the specification you are teaching or learning.

What Are Simultaneous Equations and Inequalities?

Simultaneous equations

Some real-life situations are dependent on two or more variables. If a situation is dependent on two variable, we require two equations representing the relationship between the variables.

Solving those two equations at the same time will help us find out the values of both the variables. Similarly, if the scenario is dependent on three variables, we need to solve three equations to find the values of three variables.

Equations can be solved simultaneously using two methods:

  • Solution by substitution
  • Solution by elimination


In some scenarios, the solution lies within a range of values instead of being exact. For example, x>5, y<-7, z ≤-9, p ≥-3 and many more. These are inequalities. An inequalities is solved very similar to an equation.

However, there is a difference when an inequality is multiplied or divided by a negative number.

The solutions of an inequalities can also be represented graphically.

Example: Show the inequalities y ≥ 3x + 6 & (b) y > x2 + 6

Solution: Replacing the inequality with = in y ≥ 3x + 6, we get y = 3x + 6. A solid line is used because the line is included in the solution.

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