Division of Equations

What is Division of Equations?

A reduction step in which one equation of a system is divided by another, term for term, so that a common factor cancels and a simpler relation between the unknowns remains. The step is valid only when the dividing expression is known to be non-zero, which must be established from the equations themselves before the division is carried out; if the expression can be zero, the correct move is to factorise and treat the zero case as a separate branch, because dividing removes that branch permanently.

This definition is part of the Simultaneous Equations chapter in Cambridge O Level Additional Mathematics.

Concepts related to Division of Equations

• non-zero divisor
• lost root
• case split