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Is there solution for this kind of equation

  1. Dec 17, 2007 #1
    to solve this question is possible or not

    X1Y1 = A

    X2Y2 = B

    X3Y3 = C

    X4Y4 = D

    X4Y5 = E

    HERE A,B,C,D, and E known. X and Y ` s unknown. if you divide

    X1Y1 / X2Y2 = A/B
    X1Y1 / X3Y3 = A/C
    X1Y1 / X4Y4 = A/D
    X1Y1 / X5Y5 = A/E
    X2Y2 / X3Y3 = B/C
    X2Y2 / X4Y4 = B/D
    X2Y2 / X5Y5 = B/E
    X3Y3 / X4Y4 = C/D
    X3Y3 / X5Y5 = C/E
    X4Y4 / X5Y5 = D/E

    we have 10 equation and 10 unknown, may I ask can we find each X and Y values. is iy possible.

  2. jcsd
  3. Dec 17, 2007 #2
    By X1, I assume you mean X1 and similarly for the rest. Each of your original equations are independent of each other.
    In the derived equations, even though you seem to have 10 independent equations and 10 unknowns, when solving you will find that these are in fact dependent, therefore a solution is not possible.
  4. Dec 17, 2007 #3


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    To show arunbg's point: if you divide the last two equations,
    X3Y3 / X5Y5 = C/E
    X4Y4 / X5Y5 = D/E
    you get
    X3Y3 / X4Y4 = C/D
    which is already in the list.
    No matter how you rewrite it, you will keep 5 independent equations for the 10 unknowns.
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