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Math Help - FP2 - question on simultaneous equations

  1. #1
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    FP2 - question on simultaneous equations

    Posted on Friday, 14 August, 2009 - 06:24 pm:
    hi..thanks

    Question: Find the two values of k for which the equations

    (1) 6x + 3y = 9
    (2) kx + 8y = 6

    do not have a unique solution. In both cases find the solution set for the equations

    My attempt:

    I'm looking for the values of which the coefficient matrix is zero this is 48 - 3k = 0 or k =16

    I input these into the equation and obtain

    (1') 6x + 3y = 9
    (2') 16x + 8y = 6

    or equivalently

    (1') y = 3 - 2x
    (2') y = (2/4)- 2x

    from which I conclude that the equations are not consistent, rather they represent two parallel planes that do not meet, i.e. no solution

    From here on I don't know what to do to obtain a second value of k, presumably the one where the lines are the same, i can't think that this would be true for any value of k.

    Thanks, also here's the book's answer:
    k=4. (3/2, -2t, t); k = -4, no solution (personally I think the book is bonkers)
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  2. #2
    MHF Contributor
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    France
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    Hi

    You are right

    I presume a mistake in the equations : maybe they should be
    (1) 6x + 3ky = 9
    (2) kx + 8y = 6

    The determinant of the matrix is 48 - 3kČ, which leads to k=4 or k=-4
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  3. #3
    Junior Member
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    cool..
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