6.102. $\left\{\begin{array}{l}\sqrt{2 x-y+11}-\sqrt{3 x+y-9}=3 \\ \sqrt[4]{2 x-y+11}+\sqrt[4]{3 x+y-9}=3\end{array}\right.$

The system of equations is:
\[
\left\{\begin{array}{l}
\sqrt{2 x - y + 11} - \sqrt{3 x + y - 9} = 3 \\ 
\sqrt[4]{2 x - y + 11} + \sqrt[4]{3 x + y - 9} = 3
\end{array}\right.
\]
Solution.

Let $\left\{\begin{array}{l}\sqrt[4]{2 x-y+11}=u \geq 0, \\ \sqrt[4]{3 x+y-9}=v \geq 0 .\end{array}\right.$

With respect to $u$ and $v$, the system takes the form

$$
\left\{\begin{array} { l } 
{ u ^ { 2 } - v ^ { 2 } = 3 , } \\
{ u + v = 3 }
\end{array} \Leftrightarrow \left\{\begin{array} { l } 
{ ( u - v ) ( u + v ) = 3 , } \\
{ u + v = 3 }
\end{array} \Leftrightarrow \left\{\begin{array} { l } 
{ u - v = 1 , } \\
{ u + v = 3 , }
\end{array} \text { from which } \left\{\begin{array}{l}
u=2 \\
v=1
\end{array}\right.\right.\right.\right.
$$

![](https://cdn.mathpix.com/cropped/2024_05_22_fa9db84b44b98ec0a5c7g-323.jpg?height=138&width=932&top_left_y=675&top_left_x=112)

from which

$$
\left\{\begin{array}{l}
x=3 \\
y=1
\end{array}\right.
$$

Answer: $(3 ; 1)$.