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DfE statement A19 · Algebra

Simultaneous equations

part HigherNon-calculator

Simultaneous equations is content statement A19 of the DfE GCSE mathematics subject content, in the algebra area. It is on both tiers, with a Higher-only part, and it is examined without a calculator. Below is what the specification actually requires, the 4 mistakes that cost marks on this topic most often, and practice questions written to the statement — original questions, not past papers.

What the specification says

The DfE subject content for GCSE mathematics states, verbatim: "Solve two simultaneous equations in two variables (linear/linear or linear/quadratic) algebraically; find approximate solutions using a graph." (statement A19). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.

— Department for Education, Mathematics: GCSE subject content and assessment objectives, statement A19

Tier

Both tiers, but part of it is Higher only. Foundation covers the statement except for the following, which the DfE prints in bold and reserves for Higher: "or linear/quadratic". Everything else in the statement is Foundation content.

Calculator

This is non-calculator territory. Questions on it belong naturally on Paper 1, where written method is all you have — so practise it that way rather than with a calculator to hand.

Common mistakes

  • Adding the two equations when the matching terms have the same sign, so nothing is eliminated.
  • Multiplying an equation through by a number but applying it to only some of the terms, including the constant on the right.
  • Finding one unknown and stopping. Both values are needed, and substituting back checks them.
  • In the linear/quadratic case, substituting into the quadratic the wrong way round, or losing the second pair of solutions.

Sample questions (10 of 30)

A19 · Simultaneous equationsQuestion 1 of 10 · 0 correct
Practice mode· no pressure · hints available

Algebra

A19

Advanced

Solve the simultaneous equations y = 2x − 1 and y = x² − x − 1, giving both pairs of solutions.

xy-6-5-4-3-2-1123456-12-10-8-6-4-224681012141618202224260
y = 2x − 1y = x²
💡 Hints:
Foundation worksheetHigher worksheetFoundation algebra practiceHigher algebra practice

Nearby statements

A1Algebraic notationA2Substitution into formulaeA3Expressions, equations, formulae, identities and inequalities

Questions people ask

Is simultaneous equations on Foundation or Higher?

Both, but not all of it. The parts the DfE prints in bold — "or linear/quadratic" — are Higher only; the rest is Foundation content.

Can I use a calculator for simultaneous equations?

Not on Paper 1, which is where this normally appears. Paper 1 is non-calculator for both tiers and carries the same 80 marks as each of the other two papers.

What is the single most common mistake here?

Adding the two equations when the matching terms have the same sign, so nothing is eliminated.

Are these past paper questions?

No. Every question is original, written to this DfE content statement and checked before publication. We do not host past papers or mark schemes.

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