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Math Help - Please!! Solving system

  1. #1
    ttG
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    Please!! Solving system

    Investigate for what values of k & c the following system 2x + 3y = 17, kx - y = c has either no simultaneous solution or more than one simultaneous solution.
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  2. #2
    Lord of certain Rings
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    Quote Originally Posted by ttG View Post
    Investigate for what values of k & c the following system 2x + 3y = 17, kx - y = c
    Think geometrically,for a change.
    The equations correspond to equations of a line. So searching for simultaneous solutions is searching for intersections geometrically.

    Quote Originally Posted by ttG View Post
    has either no simultaneous solution
    When will two straight lines in a plane never meet?

    Quote Originally Posted by ttG View Post
    or more than one simultaneous solution.
    When will two straight lines in a plane meet at more than one point?
    --------------------------------------------------------------------------------------------------
    Of course, you can do this using linear algebra too.

    \begin{vmatrix} 2 & 3 \\ k & -1 \end{vmatrix} = 0 implies there exists "no simultaneous solution" or "more than one simultaneous solution."
    So k = -\frac23
        kx - y = c \Rightarrow 2x+3y = -3c

    If
    -3c = 17,
    then equations are identical and we have "more than one simultaneous solution."
    else
    we have "no simultaneous solution".
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