Simultaneous Equations Topic Review summary

Key learning points

• Elimination or substitution for two linear equations.
• Linear–quadratic: solve the linear for one variable, substitute into the quadratic.
• Interpret intersections of a line and a curve geometrically.
• Check both solutions in the original equations.
• Keep algebra neat — sign errors dominate this topic.

Worked example 1 — Linear

Solve $x+y=5$, $2x-y=4$.

Working

Add to eliminate $y$.

Worked example 2 — Line & curve

$y=x+1$ meets $y=x^2$.

Working

Substitute then quadratic formula.

Worked example 3 — Elimination or substitution for two linear

Apply this idea from the Topic Review: Elimination or substitution for two linear equations.

Working

Attempt without notes, then check the answers PDF.

Worked example 4 — Linear–quadratic: solve the linear for one

Apply this idea from the Topic Review: Linear–quadratic: solve the linear for one variable, substitute into the quadratic.

Working

Attempt without notes, then check the answers PDF.

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.