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

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

3. Preview

4. Left – to – Right Elimination (aka Echelon Form)

5. Operations on a System of Equations The following operations result in an equivalent system: 1.. 2.. 3..

6. 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.

7. Example

8. 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.

9. Example

10. Assignment Pg. 505 # Exam 5? Due: November 22, 2013 @ the beginning of class.