\(A=-2x^2-10y^2+4xy+4x+4y+2016\\ A=-2x^2+4xy-4y^2+4\left(x-y\right)-2-6y^2+8y+2018\\ A=-2\left(x-y\right)^2+4\left(x-y\right)-2-6\left(y^2-\dfrac{4}{3}y\right)+2018\\ A=-2\left[\left(x-y\right)^2-2\left(x-y\right)+1\right]-6\left(y^2-2\cdot\dfrac{2}{3}y+\dfrac{9}{4}\right)+\dfrac{27}{2}+2018\\ A=-2\left(x-y-1\right)^2-6\left(y-\dfrac{3}{2}\right)^2+\dfrac{4063}{2}\le\dfrac{4063}{3}\\ A_{max}=\dfrac{4063}{2}\Leftrightarrow\left\{{}\begin{matrix}x-y=1\\y=\dfrac{3}{2}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{5}{2}\\y=\dfrac{3}{2}\end{matrix}\right.\)
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