Simultaneous Equations summary

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

Add to eliminate $y$.

Worked example 2 — Substitution

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

Working

Substitute for $y$.

Worked example 3 — Scaled elimination

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

Working

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.