7.144. $\left\{\begin{array}{l}2^{x} \cdot 3^{y}=6 \\ 3^{x} \cdot 4^{y}=12 .\end{array}\right.$
## Solution.

Dividing the second equation of the given system by the first, we get $\frac{3^{x} \cdot 4^{y}}{2^{x} \cdot 3^{y}}=\frac{12}{6}, \quad \frac{3^{x-y}}{2^{x-2 y}}=2, \quad 3^{x-y}=2^{1+x-2 y}$.

This equality is possible when

$$
\left\{\begin{array}{l}
x-y=0, \\
1+x-2 y=0
\end{array} \Rightarrow x=y, \quad 1+y-2 y=0 ; \quad y=1\right.
$$

Then $x=y=1$.

Answer: $\quad(1 ; 1)$