Algebra · Simultaneous equations
Chapter 1 · 4
The idea
Simultaneous equations — one linear, one quadratic
Why a line can meet a curve twice (so expect two solution PAIRS), why substitution is the only route in, and the bracket-squaring discipline that circle equations demand.
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Algebra · Simultaneous equations
Simultaneous equations — one linear, one quadratic
Why a line can meet a curve twice (so expect two solution PAIRS), why substitution is the only route in, and the bracket-squaring discipline that circle equations demand.
Why it works
Up to two crossing points
A line and a parabola (or circle) can cross twice — so the algebra must be allowed to produce two answers. That's the headline difference from linear pairs: the solution is up to two pairs , one per crossing point.Substitution is forced
Elimination thrives on matching shapes, but has no partner to cancel against. Instead, substitute the linear equation into the quadratic one. For and : both equal , so set them equal —Keep reading — free
The rest of the explanation, plus 2 worked examples you step through move by move.
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