maths simultaneous equation

(x+y)+(y+z)=5(x+y)(y+z)
(x+z)+(y+z)=7(y+z)(x+z)
(x+y)+(x+z)=6(z+x)(x+y)
find xyz please show working

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  1. My previous solution of x=y=z=0 works, but was derived in error.

    The other solution is
    x = 5/24
    y = 7/24
    z = 1/24

    x+2y+z = 5xy + 5xz + 5y^2 + 5yz
    x+y+2z = 7xy + 7xz + 7yz + 7z^2
    2x+y+z = 6x^2 + 6xy + 6xz + 6yz

    Now just start substituting.

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    posted by Steve
  2. both how did u solved it Sir steve

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