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Simultaneous Equations

Revise Simultaneous Equations in Algebra for GCSE Mathematics with 15 exam-style questions and 12 flashcards. This is a high-frequency exam topic, so students should expect to explain it clearly under timed conditions.

Study this topic

1

Two Equations, Two Unknowns

Introduction2

Two Methods

Key Facts3

Method 1: Elimination

Deep Dive4

Method 2: Substitution

Deep Dive5

Worked Example 1: Elimination

Notes6

Worked Example 2: Substitution

Notes7

Common Mistakes to Avoid

Exam Tips

Sample 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

Sample Questions

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

15

exam-style questions

12

revision flashcards

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