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Question 358829: How do I determine whether a system of a linear equation is independent, dependent, or inconsistent. ''Without'' Graphing.
Found 2 solutions by stanbon, neatmath:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! If slopes are different, system is independent.
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If slopes are same and intercepts are same, system is dependent.
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If slopes are same and intercepts are not the same, system is inconsistent.
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Cheers,
Stan H.
Answer by neatmath(302)  (Show Source):
You can put this solution on YOUR website! Dependent linear equations are ones which when simplified are the same equations. Example:
 and 
Notice that both equations will have the same slope, and will also be the same line! When this occurs, you will have an infinite number of solutions.
Inconsistent linear equations are ones which when simplified are parallel lines, but are NOT the same line. Example:
 and 
Notice that they do have the same slope, but have different y-intercepts, and thus, are totally different lines. When this occurs, you will have no solutions!
Independent linear equations are neither dependent nor inconsistent. Example:
and 
When this occurs you will have one and only one solution.
Simply put:
Same slope, same y-intercept are dependent linear equations.
Same slope, different y-intercept are inconsistent linear equations.
Different slopes are independent linear equations.
So check the slope, then the y-intercept and you will find out what kind of system of linear equations you are dealing with.
I hope this helps!
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