Is x=y=z=0x=y=z=0?

Algebra Level 5

{(x2)(y2)=4(y3)(z3)=9(z4)(x4)=16 \large{\begin{cases} (x-2)(y-2)=4 \\ (y-3)(z-3)=9 \\ (z-4)(x-4)=16 \end{cases}}

Let x,yx,y and zz be positive rational numbers satisfying the system of equations above, find the value of 5x+7yz5x+7y-z.

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