Learning pack · IGCSE handout

Simultaneous Equations

What's in this pack: printable worksheet PDF, matching answers PDF (IGCSE / Secure–Stretch practice). Two equations, two unknowns: elimination or substitution. Check by substituting back into both originals.

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: 23_simultaneous_equations_handout.pdf · 23_simultaneous_equations_handout_answers.pdf

Full topic summary

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

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.

🎬 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 summary.