1. Pre calculus warm up
3.11.14
C. How many solutions are there to each 3 - variable system
graphed below?
A. The graph of a 3 variable equation is a _____________?
B. What is row-echelon form?

2. Gaussian Elimination
GENERAL IDEA:
1. Forward Elimination
2. Back Substitution
GOAL:
Transform the system into Row-echelon form.
HOW:
Perform elementary row operations so that back
substitution can be easily done.

3. Elementary Row Operations
Changes done to a system of equations that still
maintain its equivalence.
There are only 3 Elementary Row Operations
1. Interchange 2 equations (or Rows)
2. Multiply one of the equations (or rows) by a
non-zero constant.
3. Add a multiple of one row to another.

4. Gaussian Elimination
Perform elementary row operations so that back
substitution can be easily done.
Suggested steps:
1. Obtain a coefficient of “1” for x in Row 1
2. Eliminate x from Row 2 and Row 3
3. Obtain a coefficient of “1” for y.
4. Eliminate y from Row 3
5. Obtain a coefficient of “1” for z – then back
substitute to solve.