7.134. $\left\{\begin{array}{l}3^{2 x}-2^{y}=725 \\ 3^{x}-2^{y / 2}=25\end{array}\right.$

Solve the system of equations:
\[
\left\{\begin{array}{l}
3^{2 x}-2^{y}=725 \\
3^{x}-2^{y / 2}=25
\end{array}\right.
\]
## Solution.

Rewrite the system of equations as

$$
\left\{\begin{array} { l } 
{ ( 3 ^ { x } - 2 ^ { y / 2 } ) ( 3 ^ { x } + 2 ^ { y / 2 } ) = 7 2 5 , } \\
{ 3 ^ { x } - 2 ^ { y / 2 } = 2 5 }
\end{array} \Leftrightarrow \left\{\begin{array} { l } 
{ 3 ^ { x } + 2 ^ { y / 2 } = 2 9 , } \\
{ 3 ^ { x } - 2 ^ { y / 2 } = 2 5 }
\end{array} \Leftrightarrow \left\{\begin{array}{l}
3^{x}=27 \\
2^{y / 2}=2
\end{array}\right.\right.\right.
$$

from which $\left\{\begin{array}{l}x=3, \\ y=2 .\end{array}\right.$

Answer: $(3 ; 2)$