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Explain how you can determine form the graph of a system of two linear equations in two variables whether it is an independent system, dependent system, or ....

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1 Answer

Ryan,
 
If the two lines are parallel to one another (which is another way of saying they have the same slope), the system is, by definition, inconsistent.
 
If the two equations turn out to be of the very same line, then they cross at infinitely many points, the system is dependent.
 
If the two lines have different slopes, they will intersect at one point, the system is independent.