SOLUTION: Determine whether the system is consistent, inconsistent, or dependent. 3x - 3y = -9 9x - 9y = -27

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Question 621480: Determine whether the system is consistent, inconsistent, or dependent.
3x - 3y = -9
9x - 9y = -27
Answer by fcabanski(1391) About Me  (Show Source):
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The three choices are not mutually exclusive. A system can be consistent and dependent if it has an infinite number of solutions.


By graphing, or with algebra, notice that both equations are the same.


Divide the first by 3 to see it's x - y = -3


Divide the second by 9: x - y = -3


Since they are the same there are an infinite number of solutions. Therefore this system is consistent and dependent.


By substitution note that (first equation)" x=y-3


Second equation 9(y-3) -9y =-27


9y - 27 -9y = -27


0=0 - denotes infinite number of solutions.

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