\(\left|2x-2\right|^{2017}+\left(3y+10\right)^{2018}=0\left(1\right)\)
Ta thấy: \(\begin{cases}\left|2x-2\right|^{2017}\ge0\\\left(3y+10\right)^{2018}\ge0\end{cases}\)
\(\Rightarrow\left|2x-2\right|^{2017}+\left(3y+10\right)^{2018}\ge0\left(2\right)\)
Từ (1) và (2) suy ra \(\begin{cases}\left|2x-2\right|^{2017}=0\\\left(3y+10\right)^{2018}=0\end{cases}\)\(\Rightarrow\begin{cases}2x-2=0\\3y+10=0\end{cases}\)
\(\Rightarrow\begin{cases}2x=2\\3y=-10\end{cases}\)\(\Rightarrow\begin{cases}x=1\\y=-\frac{10}{3}\end{cases}\)