Bài giải :

${{\left| x-4 \right|}^{2017}}+\left| y \right|=0$

Vì  $\left\{ \begin{align} & {{\left| x-4 \right|}^{2017}}\ge 0 \\  & \left| y \right|\ge 0 \\ \end{align} \right.$   nên để ${{\left| x-4 \right|}^{2017}}+\left| y \right|=0$ thì :

$\left\{ \begin{align} & {{\left| x-4 \right|}^{2017}}=0 \\ & \left| y \right|=0 \\ \end{align} \right.$

$\left\{ \begin{align} & x=4 \\  & y=0 \\ \end{align} \right.$