Fiducia TogetherSimultaneous equations
Two equations solved together to find values that satisfy both.
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.
What it is
A pair of equations in two unknowns, solved to find the values of both — for example 2x + y = 7 and x − y = 2.
Where it applies
Both tiers. Higher includes one linear and one quadratic equation.
How it works
Elimination adds or subtracts the equations to remove a variable. Substitution rearranges one and puts it into the other. Graphically, the solution is where the two lines cross.
For a linear-and-quadratic pair, substitution is nearly always the way.
How to use it in your work
Label your equations (1) and (2) and say what you are doing — "(1) − (2)" — because method marks are awarded for the steps.
Substitute your answers back into the ORIGINAL equations to check. Both must work.
A linear-quadratic pair usually has two solutions; giving one loses a mark.
Where to get help
Your teacher, your board's specification for what is on your paper, and Bitesize for worked examples. The maths song runs the topics in order.
Revise this with a song
These are ours. We write revision songs because a lot of people remember a tune when they cannot remember a page, and because revising out loud in the kitchen beats staring at a highlighter.
- The Maths Song The GCSE maths topics, in order.
Where to read more
Last reviewed 2026-08-28 by Fiducia Together · Next review due 2027-08-28
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.