IP AMaths Notes (Upper Sec, Year 3-4): 04) Simultaneous Equations
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Classical elimination, substitution, and simultaneous non-linear systems for IP AMaths problem solving.
Last updated 30 Nov 2025
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- Start Here
- 1 Toolkit
- 2 Worked example - Linear and quadratic
- 3 Worked example - Two quadratics
Q: What does IP AMaths Notes (Upper Sec, Year 3-4): 04) Simultaneous Equations cover?
A: Classical elimination, substitution, and simultaneous non-linear systems for IP AMaths problem solving.
Expect to pair a linear relation with a curve or two curves together. Sketch the solution region mentally before diving into algebra so you keep track of feasible roots.
Keep the full topic roadmap handy via our IP Maths tuition hub so you can jump into related drills, quizzes, or diagnostics as you move through these notes.
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These notes align with SEAB GCE O-Level Additional Mathematics (4049) content used in IP programmes (exams from 2025).
Status: SEAB O-Level Additional Mathematics 4049 syllabus (exams from 2025) checked 2025-11-30 - scope unchanged; remains the reference for this note.
Start Here
| Read time | What to take away |
| 1 second | Simultaneous equations are about reducing two conditions to one variable. |
| 10 seconds | Decide whether to eliminate, substitute, or subtract equations before expanding. Then back-substitute every accepted root. |
| 100 seconds | Example: if a line is paired with a quadratic, rewrite the line as y = ... first, substitute into the quadratic, solve, then find the matching y-values. |
1 Toolkit
- Linear pair: eliminate a variable via addition/subtraction or substitution.
- Linear with quadratic: substitute the linear expression into the quadratic to obtain a single-variable equation, then solve and back-substitute.
- Quadratic pair: subtract to eliminate squared terms, or complete the square to interpret geometrically.
2 Worked example - Linear and quadratic
Solve the system
