You can do this with two minipage
s, each with its own align
environment.

I made the left minipage
40% of \textwidth
and the right 60%, but you can adjust that how you like. For example, with .5\textwidth
on both minipages it looks like this:

\documentclass{article}
\usepackage{amsmath,lipsum}
\begin{document}
\lipsum[1]
\noindent\begin{minipage}{.4\textwidth}
\begin{align}
x&=1 \\
y&=1
\end{align}
\end{minipage}% <-- % symbol necessary
\begin{minipage}{.6\textwidth}
\begin{align}
z&=1\\
w&=1
\end{align}
\end{minipage}
\vspace{\baselineskip}
\lipsum[2]
\end{document}
Also, as @frabjous suggested in the comments, you could make smaller minipage
s and center
them to get the labels closer:

\noindent\begin{center}\begin{minipage}{.3\textwidth}
\begin{align}
x&=1 \\
y&=1
\end{align}
\end{minipage}\hspace{1cm}% <-- % symbol necessary
\begin{minipage}{.3\textwidth}
\begin{align}
z&=1\\
w&=1
\end{align}
\end{minipage}\end{center}