Cambridge O Level Additional Mathematics · Syllabus 4037 · Simultaneous Equations
Simultaneous Solution
What is Simultaneous Solution?
An ordered pair of values, written (x, y), that makes two equations in the same two unknowns true at the same time. Because both equations must hold together, the pair is a single indivisible answer rather than two separate results, and geometrically it is a point at which the graphs of the two equations intersect. A system may have no such pair, exactly one, or several.
This definition is part of the Simultaneous Equations chapter in Cambridge O Level Additional Mathematics.
Simultaneous Solution in context
A simultaneous solution is one ordered pair \((x,y)\) that satisfies both original equations at the same instant. In Additional Mathematics at least one of those equations is usually not a straight line, so the reduced equation is a quadratic and there is normally more than one ordered pair. Your job is to find every pair, keep each \(x\) welded to its own \(y\), and prove each pair works in both originals.