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Math Help - For which values of k are there no solutions, 1 solution, inifinite solutions.

  1. #1
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    For which values of k are there no solutions, 1 solution, inifinite solutions.

    x-y = 1
    3x - 3y = k

    1 -1 1
    3 -3 k

    1 -1 1
    0 0 k-3

    so when k doesnt equal 3 there is no solutions

    k = 3 infinite solutions

    but i cant do the one solution, is there one? or have done it wrong?

    Thanks
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  2. #2
    A Plied Mathematician
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    It looks like you've already answered your question. The problem is, the matrix you're dealing with is singular. That implies automatically, I think, that the existence of a unique solution is impossible. In other words, you've found all the possibilities. Just say there are no values of k for which the system has exactly one solution.
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  3. #3
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    The two lines are parallel. What does that tell you?
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  4. #4
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    Quote Originally Posted by Plato View Post
    The two lines are parallel. What does that tell you?
    They don't cross, so there isn't one solution, cheers
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  5. #5
    A Plied Mathematician
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    It's probably more accurate to say that the lines, represented by the system of equations you have there, are either the same line, or non-intersecting, corresponding to infinite solutions and zero solutions, respectively. Does that make sense?
    Last edited by Ackbeet; July 26th 2010 at 07:07 AM. Reason: Better Grammar.
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  6. #6
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    Quote Originally Posted by Ackbeet View Post
    It's probably more accurate to say that the lines, represented by the system of equations you have there, are either the same line, or non-intersecting, corresponding to infinite solutions and zero solutions, respectively. Does that make sense?
    Yep it does, thanks for your time.
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  7. #7
    A Plied Mathematician
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    Great. You're very welcome. Have a good one!
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