\newenvironment{ncases}[4]{%
\parbox{0.5\textwidth}{%
\begin{equation*}
#1=
\begin{cases}
#2
\end{cases}
\end{equation*}}
\hfill
\parbox{1cm}{%
\begin{eqnarray}
{}\label{#3}\\
{}\label{#4}
\end{eqnarray}}}
Note: this command only supports two equations, if needed one can extend it easily to the number you want.
2) Use that command instead of the case command:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newenvironment{ncases}[4]{%
\parbox{0.5\textwidth}{%
\begin{equation*}
#1=
\begin{cases}
#2
\end{cases}
\end{equation*}}
\hfill
\parbox{1cm}{%
\begin{eqnarray}
{}\label{#3}\\
{}\label{#4}
\end{eqnarray}}}
\begin{document}
\begin{spacing}{1.1}
\begin{ncases}
{|x|}{x, &\text{if $x\ge 0$}\\
-x,&\text{if $x\le 0$}}{pos}{neg}
\end{ncases}
For if $x\ge 0$, then by Equation~\eqref{pos}, we have $|x|=x\ge0$ and
if $x\le0$, then by Equation~\eqref{neg}, we have $|x|=-x\ge0$.
\end{spacing}
\end{document}
