Multivariable Linear Systems
Objective:
In this lesson you learned how to recognize linear systems in
rowechelon form and to use backsubstitution to solve the
systems, how to solve systems of equations by Gaussian
elimination, how to solve nonsquare systems of equations,
and how to use systems of linear equations in three or more
variables to model and solve reallife problems.
Important Vocabulary Define each term or
concept. Rowechelon form Ordered triple Row operations a Gaussian elimination Nonsquare system of equations 
I. RowEchelon Form and BackSubstitution
(Page 687) When elimination is used to solve a system of linear equations, the goal is. . . Example 1: Solve the system of linear equations.

What you should learn How to use back substitution to solve linear systems in row echelon form 
II. Gaussian Elimination
(Pages 688691) To solve a system that is not in rowechelon form, . . .
List the three row operations on a system of linear
equations that Example 3: 
What you should learn How to use Gaussian elimination to solve systems of linear equations 
III. Nonsquare Systems (Page
692) In a square system of linear equations, the number of equations in the system is __ the number of variables. If a system has more variables than equations, the system cannot have a(n) ___ . Example 4: Solve the system of linear equations.

What you should learn How to solve nonsquare systems of linear equations 
IV. Applications of Multivariable
Systems (Pages 693694) The height at time t of an object that is moving in a vertical line with constant acceleration a is given by the position equation ____ , where s is measured in feet, t is measured in seconds, v_{0} is the initial velocity, and s_{0} is the initial height. Describe a situation or application in which solving a system of multivariable linear systems is required. Example 5: Find a quadratic equation, y = ax ^{2} + b x + c , whose graph passes through the points ( 4, 36), (0, 8), and (2, 0). 
What you should learn How to use systems of linear equations in three or more variables to model and solve application problems 
Additional notes
Homework Assignment Page(s) Exercises 