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GCSE Maths: Quadratic Simultaneous Equations

Solve a linear and a quadratic equation together by substitution. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

AlgebraHigher tierAQA · Edexcel · OCR · Eduqas

What you need to know

The concepts examiners test on quadratic simultaneous equations, and what each one is really asking.

Rearrange the linear equation and substitute it into the quadratic
Solve the resulting quadratic
Pair each x value with its matching y value
Interpret the solutions as intersection points on a graph

Where marks get lost

The exam technique that separates a correct method from a correct answer.

  • Trying to eliminate rather than substitute
  • Expanding (x + 1)² as x² + 1 and losing the middle term
  • Finding both x values and only one y
  • Pairing the values wrongly, so an x is matched with the other solution's y

Quadratic Simultaneous Equations questions students ask

Is Quadratic Simultaneous Equations on the Foundation paper?

No — Quadratic Simultaneous Equations is a Higher tier topic, so it appears on Higher papers only.

What should I know before starting Quadratic Simultaneous Equations?

It builds on Simultaneous equations and Quadratics and Expanding brackets. If those feel shaky, practise them first — Quadratic Simultaneous Equations questions assume them.

What is the most common mistake in Quadratic Simultaneous Equations?

Trying to eliminate rather than substitute.

Which exam boards cover Quadratic Simultaneous Equations?

All four we support — AQA, Edexcel, OCR and Eduqas. GCSE Maths subject content is set by the DfE, so the topic is common to every board; what changes is the paper structure and the grade boundaries.