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Section 10.2: System of LINEAR equations: Three
Equations containing Three Variables
Instructor: Ms. Hoa Nguyen
(nguyen@scs.fsu.edu)
1 Geometric View of Three Linear Equations contain
ing Three Variables
Reminder of Linear Equation
:
A linear equation containing three variables
x,y
, and
z
is an equation of the form
Ax
+
By
+
Cz
=
D
, where
A,B,C
, and
D
are constants.
The graph of a linear equation containing the variables
x,y,z
is a PLANE in
xyz
space.
Thus, a system of three linear equations containing the variables
x,y,z
is THREE
PLANES in
xyz
space.
A system of three linear equations containing three variables
:
The above Figure shows 3 possible solutions of a system of three linear equations containing
three variables:
•
Exactly ONE solution (UNIQUE solution): the solution is given by the point of inter
section.
•
INFINITELY MANY solutions.
•
NO solution.
Note
: It is NOT possible for a linear system to have exactly three solutions.
A system of equations is said to be
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 Spring '11
 Nuegyen
 Linear Equations, Equations

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