6.091. $\left\{\begin{array}{l}(x-y) \cdot x y=30 \\ (x+y) \cdot x y=120\end{array}\right.$
## Solution.

After dividing the second equation of the system by the first, we get $\frac{(x+y) x y}{(x-y) x y}=\frac{120}{30}, y=\frac{3}{5} x$. From the first equation of the system, we find $\left(x-\frac{3}{5} x\right) x \cdot \frac{3}{5} x=30, x^{3}=5^{3}$, from which $x=5$; then $y=3$.

Answer: $(5 ; 3)$