7. Solve the system of equations $\left\{\begin{array}{c}x^{4}-y^{4}=3 \sqrt{|y|}-3 \sqrt{|x|} \\ x^{2}-2 x y=27\end{array}\right.$.
Solution: Write the system as $\left\{\begin{array}{c}x^{4}+3 \sqrt{|x|}=y^{4}+3 \sqrt{|y|} \\ x^{2}-2 x y=27\end{array}\right.$. The function $z=s^{4}+3 \sqrt{|s|}$ is even and, moreover, it is increasing on $[0 ;+\infty)$. Therefore, from the first equation, we find that $x=y$ or $x=-y$. Substituting $x=y$ into the second equation, we see that there are no solutions. If $x=-y$, then $x_{1}=3, y_{1}=-3 ; x_{2}=-3 ; y_{2}=3$. Answer: $\pm(3,-3)$.