\(\hept{\begin{cases}\left(x-y\right)^2+y^2=25\\\left(x+y\right)^2+x^2=26\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x^2-2xy+y^2+y^2=25\\x^2+2xy+y^2+x^2=26\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}3x^2+3y^2=1\\\left(x-y\right)^2+x=26\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x^2+y^2=\frac{1}{3}\\\left(x-y\right)^2+x=26\end{cases}}\)