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AlgebraKey Facts

Two Methods

Part of Simultaneous Equations — GCSE Mathematics

This key facts covers Two Methods 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 2 of 7 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 2 of 7

Practice

15 questions

Recall

12 flashcards

Two Methods

Method When to Use How It Works
Elimination Coefficients match or can be made to match Add or subtract equations to cancel one variable
Substitution One equation already has x= or y= Replace variable in second 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 Equations, Two UnknownsMethod 1: EliminationMethod 2: SubstitutionWorked Example 1: Elimination

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

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
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.

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Two Equations, Two Unknowns

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Method 1: Elimination