12. Solve the following system of equations:

\[
\left\{\begin{array}{l}
(x-y+1)^{3}+y=10 \\
(x-y+1)^{3}+x=11
\end{array}\right.
\]
12. Solution. By subtracting the first equation from the second term by term, we find that \(x-y=1\). Consequently, after the appropriate substitution, the system of equations will take the form:

\[
\left\{\begin{array}{l}
(1+1)^{3}+y=10 \\
(1+1)^{3}+x=11 . \text { We get: } x=3 \text { and } y=2
\end{array}\right.
\]