Displaystyle fractions in a system of equations

You could use dcases from the mathtools package

\documentclass{article}
\usepackage{amsmath}
\usepackage{mathtools}

\newenvironment{eqsys}{\begin{equation}\begin{dcases}}{\end{dcases}\end{equation}}

\begin{document}

\begin{eqsys}
 \frac{1}{2}    \\
 \frac{2}{5}
\end{eqsys}
\end{document}

Alternatively there is \dfrac from the amsmath package, which can be used instead of \displaystyle\frac25, but it sounds like this would be too manual for what you want.

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Here is how the dcases performs with @PeterGrill's test case

\begin{eqsys}
    e = 2 \frac{1}{2}\\
    e = 2 \frac{1}{2}
\end{eqsys}

A solution to make \displaystyle repeat for each equation would be to use \everymath={\displaystyle}, which is applied at the start of any math material. I renamed your original version as eqsysOLD and used it following the new version of eqsys for two purposes:

1. compare the output
2. test that the setting of \everymath is local and does not effect subsequent math material

Known Issues:

• Even though this solution illustrates how to apply a specific command to each equation, dcases provides better vertical spacing. So in this specific case the solution of @cmhughes is a better alternative.

Code:

\documentclass{article}
\usepackage{amsmath}

\newenvironment{eqsysOLD}{\begin{equation}\begin{cases}\displaystyle}{\end{cases}\end{equation}}

\newenvironment{eqsys}{\begin{equation}\everymath={\displaystyle}\begin{cases}}{\end{cases}\end{equation}}

\begin{document}
\begin{eqsys}
    e = 2 \frac{1}{2}\\
    e = 2 \frac{1}{2}
\end{eqsys}

\begin{eqsysOLD}
    e = 2 \frac{1}{2}\\
    e = 2 \frac{1}{2}
\end{eqsysOLD}
\end{document}