[ Symmetric Systems. Involutory Transformations ]

Solve the system of equations:

$$
\begin{aligned}
& x y=1 \\
& y z=2 \\
& z x=8
\end{aligned}
$$

#
From the system, it is clear that all variables have the same sign. By multiplying all the equations, we get $x^{2} y^{2} z^{2}=16$, from which $x y z=4$ or $x y z=-4$. Dividing by each of the equations, we will find all the unknowns.

## Answer

$(2,1 / 2,4),(-2,-1 / 2,-4)$.