Systems of Equations

Full topic overview

A system of equations (AS91269) is a set of equations that must all be true at the same time. Solving one means finding the values that satisfy every equation together — where two lines cross, or where three planes meet. This internal builds two reliable methods, substitution and elimination, extends them from two unknowns to three, asks you to read off whether a system has one, no, or infinitely many solutions, and applies all of it to word problems set in real New Zealand contexts.

Systems of Two Equations

Systems of Three Equations

Solving three equations in three unknowns→

Modelling with Systems

Setting up and solving systems from context→

Covers AS91269

Systems of Equations

Full topic overview

A system of equations (AS91269) is a set of equations that must all be true at the same time. Solving one means finding the values that satisfy every equation together — where two lines cross, or where three planes meet. This internal builds two reliable methods, substitution and elimination, extends them from two unknowns to three, asks you to read off whether a system has one, no, or infinitely many solutions, and applies all of it to word problems set in real New Zealand contexts.