An algebra problem by Abhijith Asokan

Algebra Level 3

Given that x,y,zx,y,z satisfy the following system of equations:-

{x+1y=73y+1z=4z+1x=1\begin{cases} x+\frac { 1 }{ y } =\frac { 7 }{ 3 } \\ y+\frac { 1 }{ z } =4 \\ z+\frac { 1 }{ x } =1 \end{cases}

What is the value of xyzxyz?

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