Simultaneous Equations 2 summary

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

Align coefficients.

Worked example 2 — Quadratic meet linear

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

Working

Set equal; solve quadratic.

Worked example 3 — Check

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

Working

Substitute back.

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.