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Math Help - pleae help finding z,x,y

  1. #1
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    pleae help finding z,x,y

    Find x,y and z if 1/x+1/y=1995,1/y+1/z=1996 dhe 1/x+1/z=1997
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  2. #2
    MHF Contributor red_dog's Avatar
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    Let \frac{1}{x}=a, \ \frac{1}{y}=b, \ \frac{1}{z}=c.

    Then \left\{\begin{array}{ll}a+b=1995\\b+c=1996\\a+c=19  97\end{array}\right.

    Solve the system, find a, b, c and then x, y, z.
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  3. #3
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    Quote Originally Posted by alternative View Post
    Find x,y and z if 1/x+1/y=1995,1/y+1/z=1996 dhe 1/x+1/z=1997
    Use the substitution

    u=\dfrac1x and v=\dfrac1y and w=\dfrac1z

    Then you have to solve the system of simultaneous equations:

    \left|\begin{array}{rccccl}u&+&v&&=&1995 \\ &v&+&w&=&1996 \\u&+&w&& =& 1997\end{array}\right.

    Afterwards re-substitute to calculate x, y, z.
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