\(\text{Ta có:}\left(x+2019\right)^{2018}\ge0với\forall x\)
\(|y-2020|\ge0với\forall y\)
\(\Rightarrow\)\(\left(x+2019\right)^{2018}+\)\(|y-2020|\ge0với\forall x,y\)
\(\text{Mà }\)\(\left(x+2019\right)^{2018}+\)\(|y-2020|=0\)\(\text{(Theo đề bài)}\)
\(\Rightarrow\hept{\begin{cases}\left(x+2019\right)^{2018}=0\\|y-2020|=0\end{cases}\Rightarrow\hept{\begin{cases}x+2019=0\\y-2020=0\end{cases}}}\)\(\Rightarrow\hept{\begin{cases}x=-2019\\y=2020\end{cases}}\)
\(\Rightarrow M=x+y=-2019+2020=1\)