6.195. $\left\{\begin{array}{l}x^{2}+y^{2}-2 x+3 y-9=0 \\ 2 x^{2}+2 y^{2}+x-5 y-1=0\end{array}\right.$

The system of equations is:
\[
\left\{\begin{array}{l}
x^{2}+y^{2}-2 x+3 y-9=0 \\
2 x^{2}+2 y^{2}+x-5 y-1=0
\end{array}\right.
\]
Solution.

From the condition $\left\{\begin{array}{l}2 x^{2}+2 y^{2}-4 x+6 y-18=0, \\ 2 x^{2}+2 y^{2}+x-5 y-1=0 .\end{array}\right.$

Subtracting the second equation of the system from the first, we get:

$-5 x+11 y-17=0$.

From this, $y=\frac{5 x+17}{11}, x^{2}+\left(\frac{5 x+17}{11}\right)^{2}-2 x+3 \cdot \frac{5 x+17}{11}-9=0 \Leftrightarrow$

$\Leftrightarrow 146 x^{2}+93 x-239=0$, from which $x_{1}=-\frac{239}{146}, x_{2}=1 ; y_{1}=\frac{117}{146}, y_{2}=2$.

Answer: $:\left(-\frac{239}{146} ; \frac{117}{146}\right),(1 ; 2)$