SOLUTION: Without graphing, classify the following system as independent, dependent, or inconsistent. Both of these are part of the same system, I just don't know how to mark them as such

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Without graphing, classify the following system as independent, dependent, or inconsistent. Both of these are part of the same system, I just don't know how to mark them as such      Log On


   

Question 1118737: Without graphing, classify the following system as independent, dependent, or inconsistent.
Both of these are part of the same system, I just don't know how to mark them as such.
-x-2y=-7
5x-y=2
A) Independent
B) Dependent
C) Inconsistent
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52793) About Me  (Show Source):
You can put this solution on YOUR website!
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Answer.   Independent. 


    It means that the system has a unique solution.


There are many ways to see it.


One way is to notice that the co-named coefficients of the system are not proportional.


Another way to see and to express it is to notice that the determinant of the system is not zero.


If you want more info and explanations, look into my lesson
    - Geometric interpretation of a linear system of two equations in two unknowns
in this site.


Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The slopes are not equal --> independent.
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If the slopes are not equal, there is an intersection, which is a unique solution.