81. Find the sets $X$ and $Y$ from the system of equations

$$
\left\{\begin{array}{l}
X \cup Y=A \\
X \cap A=Y
\end{array}\right.
$$

where $A$ is a given set.
$\triangle$ From the first equation of the system, it follows that $X \subset A$. Then $X \cap A=X$, which means the second equation becomes $X=Y$. In this case, from the first equation we get: $X=Y=A$.

Verification shows that the values $X=A$ and $Y=A$ we found satisfy the given system of equations.

Answer: $X=Y=A$.