Determine all possible value(s) for "k" so the system is inconsistent?

9x - 7ky + 3k = 0

kx - 7y - 7 = 0

1 Answer

  • 8 years ago
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    The system is

    9x - 7ky = -3k

    kx - 7y = 7

    This can be written as AX = b in matrix form with b = [-3k 7]^T (T for transpose), X = [x y]^T and A is the 2x2 coefficients' matrix. Since b is nonzero, for the system to be inconsistent we need detA = 0 which gives us: -63 + 7k^2 = 0. Hence k^2 = 9 or k = + or -3 (the only two such values.) Graphically speaking, for k = +3 or -3 both of the lines have the same slope so they are parallel and never meet.

    P.S. In a very special case, if the two lines had overlapped, then the system would have been consistent despite the equality of slopes. That would have happened if and only if 7 = -3k or k = -7/3, which is not the case for the problem we have in hand.

    Source(s): P.P.S. This question should have been posted in the mathematics section....
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