pc c7 s3 blank notes.notebook
7.3 Day 1 Graphical Interpretation of Three Variable Systems
pc c7 s3 blank notes.notebook
LESSON 7.3 Row­Echelon Form
The method of elimination can be applied to a system of linear equations in more than two variables to solve the system.
The goal with more than two variables is to rewrite the system in a form to which back­substitution can be applied.
System of Three Linear Equations in Three Variables
Equivalent System in Row­Echelon Form
Row-Echelon Form - like the second system that has a "stair step"
pattern with leading coefficients of 1.
pc c7 s3 blank notes.notebook
Gaussian Elimination
To obtain a system that is equivalent to the given system (has the same solution) but is in Row­Echelon Form, you must use the elementary row operations.
pc c7 s3 blank notes.notebook
Using Back Substitution in Row-Echelon Form
Equation 1
Equation 2
Equation 3
pc c7 s3 blank notes.notebook
Example
Solve the system of linear equations.
Equation 1
Equation 2
Equation 3
pc c7 s3 blank notes.notebook
7.3 Day 2
Inconsistent systems
Example
Solve the system of linear equations.
Graph
pc c7 s3 blank notes.notebook
Example
Solve the system of linear equations.
Graph
pc c7 s3 blank notes.notebook
Example
Nonsquare System
A System with Fewer Equations than Variables
Let z=a
Solve the system of linear equations.
Move when done
Graph
Attachments
grapher.exe