7.271. $\left\{\begin{array}{l}3^{x} \cdot 2^{y}=972 \\ \log _{\sqrt{3}}(x-y)=2 .\end{array}\right.$
## Solution.

Domain of definition: $x-y>0$.

From the second equation of the system, we find $x-y=3, x=y+3$. Substituting this value of $x$ into the first equation, we get $3^{y+3} \cdot 2^{y}=972$, $27 \cdot 3^{y} \cdot 2^{y}=972,6^{y}=6^{2}$, from which $y=2$. Then $x=5$.

Answer: $(5 ; 2)$.