Learning pack · IGCSE handout

Simultaneous Equations 2

What's in this pack: printable worksheet PDF, matching answers PDF (IGCSE / Secure–Stretch practice). Harder simultaneous systems may need scaling both equations or handling fractional coefficients before eliminating.

Resources at the top · full summary · videos with short notes below.

🎒 Resources in this pack

Jump straight to the printable files, or scroll to the summary and videos.

Scaffolded Learning Sheet — attempt the worksheet, then use the Answers for a full written solution.

📝 Open Learning Sheet ✅ Open answers 🎬 More topic videos (6)📖 Full summary

Files: 46_simultaneous_equations_2_handout.pdf · 46_simultaneous_equations_2_handout_answers.pdf

Full topic summary

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

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.

🎬 Topic videos

Beautiful Visual Explanation of Completing the Square
Eddie Woo · 4 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Introduction to Matrices (1 of 3: Systems of Linear Equations)
Eddie Woo · 5 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Math Antics - Basic Inequalities
Math Antics · 13 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Is there an equation for a triangle?
Stand-up Maths · 16 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
Why is there no equation for the perimeter of an ellipse‽
Stand-up Maths · 21 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
Behold all-new equations for triangles!
Stand-up Maths · 22 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.

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Browse the hub Learning Packs & Summary, or open the compact Simultaneous Equations 2 summary.