6.079. $\left\{\begin{array}{l}x^{3}+y^{3}=9, \\ x y=2 .\end{array}\right.$
## Solution.

Rewrite the system as

$$
\left\{\begin{array} { l } 
{ x ^ { 3 } + \frac { 8 } { x ^ { 3 } } = 9 , } \\
{ y = \frac { 2 } { x } }
\end{array} \Leftrightarrow \left\{\begin{array}{l}
x^{6}-9 x^{3}+8=0, \text { where } x \neq 0 \\
y=\frac{2}{x}
\end{array}\right.\right.
$$

From the first equation, we get $x_{1}^{3}=1$ or $x_{2}^{3}=8$, hence $x_{1}=1$, $x_{2}=2$. Then $y_{1}=2, y_{2}=1$.

Answer: $(1 ; 2)(2 ; 1)$