Unit Overview

Simultaneous Equations

CIE IGCSE Additional Mathematics· 5 min read 📊 5-7% of total exam marks

1. Unit at a glance

The unit follows a structured learning path focused on the specific simultaneous equation type required for the 0606 syllabus. You will first learn the substitution method to combine equations into a single solvable quadratic, then apply this skill to context-based and graphical interpretation problems.

This unit contains the following core sub-topic:

Simultaneous Equations (One or Both Non-Linear)

Master substitution and elimination to solve simultaneous equations where one or both equations are non-linear, including graphical interpretation and real-world context applications.

★★⏱ 12 min

2. Common Pitfalls

Wrong move:

Forgetting to substitute solved x/y values back into the original linear equation to find the corresponding second variable

Why:

This leaves solutions incomplete, leading to lost marks even if you correctly solved the intermediate quadratic equation

Correct move:

Always substitute each quadratic root back into the rearranged linear equation to get full (x,y) solution pairs, then verify pairs satisfy both original equations

Wrong move:

Making rearrangement errors when isolating a variable from the linear equation before substitution

Why:

Small arithmetic errors during rearrangement propagate through the rest of your working, leading to incorrect quadratic roots and final solutions

Correct move:

Double-check your linear equation rearrangement before substituting it into the non-linear equation to catch avoidable calculation errors early

3. Quick Reference Cheatsheet

Key Concept/Formula	Description
Substitution Step	Rearrange the linear equation to make $x$ or $y$ the subject, then substitute this expression into the non-linear equation
Quadratic Form	After substitution, you will get a quadratic of form $a x^{2} + b x + c = 0$ , solvable via factorisation, completing the square, or quadratic formula
Solution Pairs	Each root of the resulting quadratic corresponds to one (x,y) solution pair for the original simultaneous equations
Graphical Interpretation	Solutions correspond to the intersection points of the line (linear equation) and curve (non-linear equation) on a coordinate plane
Context Problem Rule	Reject any solution that is impossible in the problem context (e.g. negative length, negative time) even if it satisfies the equations

What's Next

Begin your learning for this unit by accessing the core sub-topic below, which includes step-by-step annotated examples and exam-style practice problems for one linear/one non-linear simultaneous equations. Once you have mastered this unit, you will progress to the next algebra unit covering linear and quadratic inequalities.