Systems of Linear Equations in Three Variables

The general form of a linear equation in three variables

ax + by + cz = d, where a, b and c are not equal to zero

A linear equation

An equation where the power of the variable is 1

Solutions to systems of linear equations in three variables

-One solution -Infinite solutions -No solution

Geometrically, a linear equation in three variables forms a plane in a three dimensional space

One solution

The planes intersect at only one point

Infinite solutions

The planes intersect in a straight line

No solution

The planes do not intersect at any point

Methods used to solve systems of linear equations in three variables

-Elimination method -Substitution method

A non-linear equation

An equation which has at least one variable whose power is not 1

The methods used to solve simultaneous equations

-Elimination -Substitution -Graphical representation methods