SOLUTION: What is the difference between: independent and dependent and consistent and inconsistent?

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Question 72567: What is the difference between: independent and dependent and consistent and inconsistent?
Answer by rmromero(383) About Me  (Show Source):
You can put this solution on YOUR website!


What is the difference between: independent and dependent 



Independent System. The graphs of the equations are different.



Example: 

graph+%28200%2C+200%2C+-4%2C5%2C+-5%2C+6%2C+3x-2%2C+3x%2B5%29



Notice that the lines are different so the system is Independent



Dependent System. The graphs of the equations are the same.



Example



graph+%28200%2C+200%2C+-4%2C5%2C+-5%2C+6%2C+3x%2B2%2C+3x%2B2%29





consistent and inconsistent?



Consistent System. System with at least one solution.



Example:

graph+%28200%2C+200%2C+-4%2C5%2C+-5%2C+6%2C+3x-2%2C+6x-4%29



There is one intersection so the system is consistent.



Inconsistent System. A system with no solution.



Example:

graph+%28200%2C+200%2C+-4%2C5%2C+-5%2C+6%2C+3x-2%2C+3x%2B5%29



Notice that the graph don't have intersection so there is no solution and 

the system is inconsistent