Non-Linear Simultaneous Equations
The Intersector — Where Lines Meet Curves
LOGIC TRACK
Isolate y in the linear equation. Stuff it into the quadratic. Solve the resulting quadratic for x.
Found x₁ and x₂? You aren't done! Plug them back into the LINEAR equation to find y₁ and y₂. Write BOTH coordinate pairs.
Don't expand (x − 1)² as x² − 1. It's x² − 2x + 1. Forgetting the middle term costs you 2+ marks!
A line crossing a parabola gives 0, 1, or 2 solutions. A line crossing a circle also gives 0, 1, or 2. If the discriminant < 0, the line misses entirely!
DYNAMIC SOLVER — Step-by-Step Mark Scheme Working
Identify the equations
Eq①: y = x²
Eq②: y = 2x + 3
Substitute: set Eq① = Eq②
Rearrange to = 0
Factorise and solve for x
Find y values (the Double Dip!)
EXAMINER TRAP ALERT
❌ WRONG: Expanding (x − 1)² as x² − 1 (forgetting the middle term −2x).
✓ CORRECT: (x − 1)² = x² − 2x + 1. Always use FOIL or the identity (a − b)² = a² − 2ab + b².
Frequency: Very Common | Mark Impact: 2-4 marks | Paper: 1H & 2H
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