7.135. $\left\{\begin{array}{l}\lg \left(x^{2}+y^{2}\right)=2, \\ \log _{2} x-4=\log _{2} 3-\log _{2} y .\end{array}\right.$

The system of equations is:
7.135. $\left\{\begin{array}{l}\lg \left(x^{2}+y^{2}\right)=2, \\ \log _{2} x-4=\log _{2} 3-\log _{2} y .\end{array}\right.$
## Solution.

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

From the first equation of the system, we have $x^{2}+y^{2}=100$. From the second equation of the system, we find $\log _{2} \frac{x}{16}=\log _{2} \frac{3}{y}$, from which $\frac{x}{16}=\frac{3}{y}$, $x=\frac{48}{y}$. Further, we get $\left(\frac{48}{y}\right)^{2}+y^{2}-100=0, y^{4}-100 y^{2}+2304=0$, from which $y_{1,2}= \pm 6, y_{3,4}= \pm 8 ; y_{2}=-6$ and $y_{4}=-8$ do not satisfy the domain of definition. Then $x_{1}=8, x_{2}=6$.

Answer: $\quad(8 ; 6)(6 ; 8)$.