IP AMaths Notes (Upper Sec, Year 3-4): 04) Simultaneous Equations

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.

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.

Worked example 1 - Linear and quadratic

Solve the system $2x + y = 7$ and $x^{2} + xy = 12$