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#47

Constructing and solving linear and quadratic simultaneous equations

Algebra · Grade 4–6

Strand: Algebra Substrand: Simultaneous equations Sparx code: U269 Sparx levels: 5 Tier: Higher Only

Key steps (method)

  • Write the two equations neatly and decide on elimination or substitution.
  • If eliminating, multiply one/both equations so one variable has matching coefficients.
  • Add/subtract the equations to eliminate that variable.
  • Solve the resulting single-variable equation.
  • Substitute back to find the other variable.
  • Check both values satisfy both original equations.

Common mistakes

  • Multiplying one side of an equation but forgetting to multiply the other side.
  • Sign mistakes when subtracting equations.
  • Forgetting to substitute back for the second variable.
  • Not checking the solution in both equations.

Quick notes

  • If you get stuck, try a simpler version of the problem first or plug in easy numbers to test your method.
  • For multi-step questions, label each step and keep intermediate results.
  • For exam questions, always aim to make your work “mark-scheme readable”.

Self-assessment

  • Can I define it? Write a one-sentence definition of Constructing and solving linear and quadratic simultaneous equations (or the key term in the question).
  • Can I do it? Do 3 questions: one easy, one standard, one harder. Don’t look at notes until you’ve tried.
  • Can I explain it? In 2–3 sentences, explain why the method works (or what would go wrong with a common mistake).
  • Can I check it? State one quick check (estimate, units, sign, reasonableness).

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