\(B=\dfrac{9}{5}x^2-6xy+5y^2+\dfrac{6}{5}x^2+2x+2021\)
\(=\dfrac{1}{5}\left(3x-5y\right)^2+\dfrac{6}{5}\left(x+\dfrac{5}{6}\right)^2+\dfrac{12121}{6}\ge\dfrac{12121}{6}\)
\(B_{min}=\dfrac{12121}{6}\) khi: \(\left\{{}\begin{matrix}x+\dfrac{6}{5}=0\\3x-5y=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=-\dfrac{6}{5}\\y=-\dfrac{18}{25}\end{matrix}\right.\)