Topic summary · IGCSE handout

Simultaneous Equations 2 summary

Harder simultaneous systems may need scaling both equations or handling fractional coefficients before eliminating.

Open Learning Sheet — Simultaneous Equations 2 Download Simultaneous Equations 2 answers PDF

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Key learning points

Scale equations so one variable’s coefficients match exactly.
Watch signs when subtracting: distribute the minus across every term.
Word problems: define variables clearly before writing equations.

Worked example 1 — Scaled elimination

Solve $2x+3y=12$ , $x+y=5$ .

Working

x=3,\ y=2

Align coefficients.

Worked example 2 — Quadratic meet linear

Solve $y=x^2$ , $y=2x+3$ .

Working

x=3\text{ or }-1

Set equal; solve quadratic.

Worked example 3 — Check

Verify $x=3,y=9$ in $y=2x+3$ .

Working

2\cdot3+3=9

Substitute back.

Scaffolded Learning Sheet and answers (PDFs)

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Open Learning Sheet Answers PDF

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