3.4: Solving Systems of Linear Equations in Three Variables

The elimination method for a three-variable system

1. rewrite the linear equation in three variables as a linear system in 2 equations by using the elimination method 2. solve the new linear system for both of its variables (solve for one variable, plug that value into the ORIGINAL TWO (2) VARIABLE EQUATION and solve for the second value) 3. use the two values found in step 2 (yeah, it's kinda a step 3 as well) and substitute it into the linear system in THREE variables

infinite solutions....

1. rewrite the system (with three variables) as a linear system in two variables 2. solve the new linear system for both of its variables 3. when solving step 2, and you get the solution [0=0] then the system had infinite solutions

ordered triple (ice cream!... sadly, no)

a coordinate in three variables (x, y, z)

system of three linear equations

a system made up of 3 linear equations in 3 variables

Linear equation in three variables

an equation of the form: ax+by+cz=d where a,b,c are not all zero

also can be done by substitution...

review packet

solution of a system of three linear equations

the solution is the value of the three variables that make each equation true