Systems of Equations
(Categorizing)
There is a solution
There is no solution
CONSISTENT
Dependent
Independent
Infinite Solutions
Exactly One Solution
(Coinciding)
INCONSISTENT
(Intersecting)
Independent
No Solution
(Parallel)
 Consistent I Inconsistent tells you if there is a solution or not.
 Independent I Dependent tells you how many lines there are:

Independent = 2 separate lines

Dependent = 1 line
(HINT: Coinciding lines are actually the same line)
The Academic Support Center at Daytona State College (Math 27 pg 1 of 2)
SYSTEMS OF TWO EQUATIONS
(Solutions)
Where are the equations - or lines - touching?
Three Scenarios:
Intersecting
Lines
Coinciding
Lines
Parallel
Lines
Touching
in one place
Touching
everywhere
Never
touching
Independent
Dependent
Independent
Consistent
Consistent
Inconsistent
One solution
Infinite solutions
No solution
You will get an xvalue and a y-value,
such as:
You will get an
answer that looks
something like:
You will get an
answer that makes
no sense, such as:
x = 5 and y = –2
0 = 0 or 2 = 2
The Academic Support Center at Daytona State College (Math 27 pg 2 of 2)
O=4