11.3. Solve the system of equations $\left\{\begin{array}{l}\sqrt{1-3 x}-1=\sqrt{5 y-3 x} \\ \sqrt{5-5 y}+\sqrt{5 y-3 x}=5 .\end{array}\right.$
Answer. $\left(-\frac{8}{3},-\frac{4}{5}\right)$.

Solution. Introduce new variables $u=\sqrt{1-3 x}, v=\sqrt{5 y-3 x}, w=$ $\sqrt{5-5 y}$.

The system can be rewritten as $\left\{\begin{array}{l}u-1=v, \\ v+w=5\end{array}\right.$ where $u \geq 0, v \geq 0, w \geq 0$.

Notice that $u^{2}-v^{2}-w^{2}=1-3 x-5 y+3 x-5+5 y=-4$ and $u=v+1, w=5-v$.

We obtain the quadratic equation $(v+1)^{2}-v^{2}-(5-v)^{2}=-4$, solving which we find the roots $v_{1}=2, v_{2}=10$.

If $v_{1}=2$, then $u_{1}=3, w_{1}=3$, and we get the system of equations

$$
\left\{\begin{array}{l}
1-3 x=9 \\
5-5 y=9
\end{array}\right.
$$

Therefore, $x_{1}=-\frac{8}{3}, y_{1}=-\frac{4}{5}$.

If $v_{2}=10$, then $u_{2}=11, w_{2}=-6<0$ and the system has no solution.