You can use the \alt environment to include the equation when you want and increment the counter when you don't:
\documentclass{beamer}
\begin{document}
\begin{frame}
\alt<1>{% do this in frame 1
\begin{align}
equation 1
\end{align}
}{% do this not in frame 1
\stepcounter{equation}
}
\only<2>{
\begin{align}
equation 2
\end{align}
}
\end{frame}
\end{document}
If the longest constraint needs to be flushed to the right margin, you could use a tabular* environment with two centered columns; something along these lines (change the lengths according to your needs):
\documentclass[reqno]{amsart}
\usepackage{array}
\newlength\MyIndent
\setlength\MyIndent{10em}
\begin{document}
\vspace{\abovedisplayskip}
\noindent\begin{tabular*}{\textwidth}{@{\hspace{\MyIndent}}>{$}c<{$}@{\extracolsep{\fill}}
>{$}c<{$}@{}}
a^2 + b^2 = ab & (a \in \{z,y,x,w,v,u\},\ b \neq 0) \\
a + b = c & (a \in \{z,y\},\ b = 0) \\
\end{tabular*}\par
\vspace{\belowdisplayskip}
\end{document}
If the longest constraint doesn't need to be flushed to the right margin, a simple array environment will do the job (change the lengths according to your needs):
\documentclass[reqno]{amsart}
\begin{document}
\[
\begin{array}{@{\hspace{7em}}c@{\hspace{3em}}c}
a^2 + b^2 = ab & (a \in \{z,y,x,w,v,u\},\ b \neq 0) \\
a + b = c & (a \in \{z,y\},\ b = 0) \\
\end{array}
\]
\end{document}
Best Answer
You can go a simple way with
or with a fancier approach (see How to move amsmath equation label into LHS margin? for motivation)