KS4 / GCSE · Mathematics — Higher
Simultaneous Equations
What is it
At Higher tier, simultaneous equations extend to pairs involving one linear and one quadratic equation, solved using substitution, and typically producing two pairs of solutions.
Why it matters
Linear-quadratic simultaneous equations connect algebra directly to graphs — the solutions are exactly the coordinates where a line and a curve intersect, making this topic a bridge between algebraic and graphical thinking.
Exam tip
Always substitute the linear equation into the quadratic one, not the other way around — attempting to substitute the quadratic into the linear equation leads to unnecessarily complicated algebra almost every time.
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