7.274. $\left\{\begin{array}{l}\left(\log _{a} x+\log _{a} y-2\right) \log _{18} a=1, \\ 2 x+y-20 a=0 .\end{array}\right.$
## Solution.

Domain of definition: $\left\{\begin{array}{l}x>0, \\ y>0, \\ 0<a \neq 1 .\end{array}\right.$

From the first equation of the system, we get $\log _{a} \frac{x y}{a^{2}}=\log _{a} 18 \Leftrightarrow$ $\Leftrightarrow \frac{x y}{a^{2}}=18, x y=18 a^{2}$. The system has the form $\left\{\begin{array}{l}x y=18 a^{2}, \\ y=20 a-2 x\end{array} \Rightarrow y=20 a-2 x\right.$, $x(20 a-2 x)=18 a^{2}, x^{2}-10 a x+9 a^{2}=0, x_{1}=a, x_{2}=9 a$. Then

$y_{1}=20 a-2 a=18 a, y_{2}=20 a-18 a=2 a$.

Answer: $(a ; 18 a),(9 a ; 2 a)$, where $0<a \neq 1$.