Mat 150 – Class #26 Topics: Systems of Linear Equations in Three Variables

What does a system of three variables mean? When equations of this form are graphed in three-dimensional coordinate system, their graphs are planes.

Preview

Left – to – Right Elimination (aka Echelon Form)

Operations on a System of Equations The following operations result in an equivalent system:

Nonunique Solutions Inconsistent System : When a system of three linear equations in three variables has no solution, the graphs of the equations will not have a common intersection.

Example

Nonunique Solutions Dependent System: When a system of three equations in three variables has infinitely many solutions, the graphs of the equations may be planes that intersect in a line.

Example

Assignment Pg. 505 # Exam 5? Due: November 22, the beginning of class.