Cambridge O Level Additional Mathematics · Syllabus 4037 · Simultaneous Equations
Excluded Value
What is Excluded Value?
A value of an unknown for which one of the original equations is undefined, most commonly a value that would make a denominator zero. Excluded values must be written down before the denominators are cleared, because multiplying through produces a polynomial equation that is defined at those values even though the original system is not; any candidate solution that lands on an excluded value is therefore an artefact of the clearing step and must be rejected rather than reported.
This definition is part of the Simultaneous Equations chapter in Cambridge O Level Additional Mathematics.
Common mistakes with Excluded Value
- “\((x-2)(x+7)=0\), and \(x=2\) looks right, so \(x=2\).” WHY IT FAILS A root is discarded only when something in the question forbids it — a stated restriction, an excluded value, or a context such as a length. “It looks nicer” is not one of those. FIX Carry both roots to the end. If one must go, name the condition that removes it in writing.
Questions students ask about Excluded Value
Why do I have to state excluded values before clearing denominators?
Because multiplying through by \(xy\) produces a polynomial equation that is defined at \(x=0\) and \(y=0\), even though the original system is not. The cleared equation is only equivalent to the original where \(xy\neq0\), so it can hand you candidates the original never permitted. Write \(x\neq0,\ y\neq0\) first, do the algebra, then reject any candidate that lands on an excluded value. Exclusions first, algebra second, exclusions again last.