Topic summary · IGCSE handout

Simultaneous Equations summary

Two equations, two unknowns: elimination or substitution. Check by substituting back into both originals.

Open Learning Sheet — Simultaneous Equations Download Simultaneous Equations answers PDF

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Key learning points

Elimination: make one coefficient match, then add/subtract.
Substitution: rearrange one equation and replace in the other.
Graphically: intersection of two lines.

Worked example 1 — Elimination

Solve $x+y=7$ , $x-y=1$ .

Working

x=4,\ y=3

Add to eliminate $y$ .

Worked example 2 — Substitution

Solve $y=2x+1$ , $x+y=7$ .

Working

x=2,\ y=5

Substitute for $y$ .

Worked example 3 — Scaled elimination

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

Working

x=3,\ y=2

Match coefficients, then subtract.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.

Open Learning Sheet Answers PDF

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