AlgebraIntroduction

Two Equations, Two Unknowns

Part of Simultaneous Equations · GCSE GCSE Mathematics revision

This introduction covers Two Equations, Two Unknowns within Simultaneous Equations for GCSE Mathematics. Revise Simultaneous Equations in Algebra for GCSE Mathematics with 15 exam-style questions and 12 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 1 of 8 in this topic. Use this introduction to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 1 of 8

Practice

15 questions

Recall

12 flashcards

Two Equations, Two Unknowns

If I tell you x + y = 10, can you find x and y? No! There are infinite possibilities (1+9, 2+8, 3+7...). But if I ALSO tell you x - y = 4, suddenly there's only ONE answer: x=7, y=3. Two equations with two unknowns can be solved - and the answer is where the two lines cross!

Visual: Two Methods for Solving

Diagram showing simultaneous equations as intersecting lines on a graph (solution is the crossing point), plus two solving methods: Elimination (add/subtract equations to cancel one variable) and Substitution (replace one variable with expression from other equation).

Keep building this topic

Read this section alongside the surrounding pages in Simultaneous Equations. That gives you the full topic sequence instead of a single isolated revision point.

Two Methods Method 1: Elimination Method 2: Substitution

Practice Questions for Simultaneous Equations

Which method is most efficient for solving the following simultaneous equations? 5x + 2y = 14 3x + 2y = 10

A. Substitution — rearrange the first equation for x, then substitute into the second.
B. Elimination — subtract the equations directly because the y-coefficients are already equal.
C. Elimination — multiply both equations by 5 and 3 respectively to match the x-coefficients.
D. Trial and improvement — test integer values of x and y until both equations are satisfied.

1 markfoundation

Ali solves the simultaneous equations 5x + y = 17 and x - y = 1 by elimination. Ben says he can also use substitution by rearranging x - y = 1 to get x = y + 1. Explain how elimination works for these two equations and state one advantage of Ben's substitution approach.

3 marksstandard

Quick Recall Flashcards

What are simultaneous equations?

Two or more equations that share the same variables. Solving them finds the values of those variables that satisfy ALL equations at the same time.

Steps for the elimination method

1. Match one set of coefficients (multiply if needed) 2. Same signs: subtract the equations 3. Different signs: add the equations 4. Solve for the remaining variable 5. Substitute back to find the other variable

15 questions on Simultaneous Equations — practise free

Instant marking, adaptive difficulty, and 12 spaced repetition flashcards. Free until your GCSEs.

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Simultaneous Equations

Two Methods