Aligning numbering in a system of equation so it's centered

Not too beautifull, but gives the desired effect:

\documentclass{amsart}

\begin{document}

\newlength\Ilength
\settowidth{\Ilength}{I}
\[
\begin{cases}
2y+4x=9 & \text{\hspace{0.5\Ilength}(I)} \\ 3x-2x=10 & \text{(II)}
\end{cases}
\]


\end{document}

You can be bold and redefine cases to take an optional argument for specifying the alignment in the second column:

\documentclass{article}
\usepackage{amsmath}

\makeatletter
\renewcommand\env@cases[1][l]{%
  \let\@ifnextchar\new@ifnextchar
  \left\lbrace
  \def\arraystretch{1.2}%
  \array{@{}l@{\quad}#1@{}}%
}
\makeatother

\begin{document}
Here is a system
\[
\begin{cases}[c]
2y+4x=9   & \text{(I)} \\
3x-2x=10 & \text{(II)}
\end{cases}
\]
and here a famous function
\[
f(x)=\begin{cases}
0 & \text{if $x$ is rational} \\
1 & \text{if $x$ is irrational}
\end{cases}
\]

\end{document}

Explanation: in the original definition of \env@cases there is

  \array{@{}l@{\quad}l@{}}%

so we can easily change the second l to be what we like more.

---

If you prefer to use systeme, as suggested in another answer, here's the way:

\documentclass{article}
\usepackage{systeme}

\begin{document}

\[
\syscodeextracol{\quad\hfil}{\hfil\hfil}
\systeme{
2y+4x=9@(I),
3x-2y=10@(II)
}
\]

\end{document}

For automatically numbered equations, here's the trick:

\[
\syscodeextracol{\quad\hfil}{\hfil\hfil}
\systeme{
2y+4x=9@(\uppercase\expandafter{\romannumeral*}),
3x-2y=10@(\uppercase\expandafter{\romannumeral*})
}
\]

Don't try to reinvent the wheel.

\documentclass[preview,border=12pt,varwidth]{standalone}
\usepackage{systeme,mathtools}

\syscodeextracol{\quad\hfill}{\hfill}
\sysautonum*{(\uppercase\expandafter{\romannumeral*})}

\begin{document}
\abovedisplayskip=0pt\relax% don't use this line in your production.
\[
\systeme{
2y+4x=91,
3x-2y=10}
\]
\end{document}

With systeme package, you will get 2 advantages:

1. The coefficients of the system of equations will be automatically arranged. We typed

   2y+4x=9
   3x-2y=10
   

   but they will be rendered as

   4x+2y=9
   3x-2y=10
   

2. The equation numbers will be automatically generated without our awareness.