A certain $y$ is determined by $x$ and $z$.
If I would keep $z$ constant at $80$, the relationship between $y$ and $x$ is $$y=17,0722/x.$$ If I would keep $x$ constant at $1$, the relationship between $y$ and $z$ is
$$y=(-0,3712\cdot z+1395,83)/(z+0,0177).$$
Is there a way to find the relationship between $y$, $x$ and $z$?
No, not without further information: You could define $y$ by your given equations and take it to by whatever you want at, say $x = 60$, $z = 60$, without interfering with what happens at $x = 1$ or at $z = 80$. As a side remark, your two relationships give slightly different results when $x = 1$ and $z=80$ (the first one giving $17,0722$, and the second one something closer to $17,073$).