Solving simultaneous equations algebraically

Simultaneous equations are a fundamental algebraic technique where you solve two or more equations together to find values that satisfy all equations at once. In AQA GCSE Maths, this topic appears in Paper 2 (Calculator) and Paper 3 (Calculator), typically worth 3-5 marks per question. There are three main methods for solving simultaneous equations: **1. Elimination Method** - Add or subtract equations to eliminate one variable **2. Substitution Method** - Rearrange one equation and substitute into the other **3. Graphical Method** - Plot both lines and find the intersection point Common question types include: - Two linear equations (most common at Foundation and Higher) - One linear and one quadratic equation (Higher tier only) - Word problems requiring you to form the equations first - Contextual problems involving costs, quantities, or measurements Key exam tips: - Always show your working clearly - method marks are available even if the final answer is wrong - Check your answer by substituting back into both original equations - For elimination, make sure coefficients match before adding/subtracting - Label your answers clearly (e.g., x = 3, y = 2)