Jane J.

asked • 07/20/16

Inconsistent equations

The system of equations below is inconsistent
2x - 3y=9
Ax - by=7

Jason L.

(A,B) would have to be a linear combination of (2,3). Easy way would be a = 2 and b = 3.  Then your system would be 2x - 3y = 9 = 7, which would make it inconsistent.
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07/20/16

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Hassan O. answered • 07/20/16

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Jason is correct! for the system to be inconsistent (or has no solutions) is for the lines to be parallel
so if a=2 and b=3 you would get a parallel lines. However 2 and 3 are not the only possible A and B to make the system inconsistent. Multiples of 2 and 3 as well will make the system inconsistent. For example 4 and 6, or 8 and 12 an so on...
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Jane J.

I missed part of the question 
A/b=?
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07/20/16

Hassan O.

Jane that is asking for the the slope
so if we want the system to have no solution A/B should equal to 2/3
2/3 is the slope of the first equation (line 1)
when a system is not consistent the two lines must be parallel also that means the same slope
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07/20/16

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