[Tex/LaTex] Aligned equations with multiple tags per line

Question

I would like to typeset something like this:

except that instead of having just one tag per line, I want one tag per equation (A1, A2, A3, B1, B2, B3), with each tag appearing to the right of its equation. The amsmath align* environment doesn't let me use \tag more than once per line.

I tried using multicols, but it was very fiddly and I couldn't get the alignment right, so I'm hoping there's a way similar to using align.

Here's a mwe:

\documentclass{article}
\usepackage{amsmath}
\begin{document}

\begin{align*}
 x &= x + 1     &    z &= \frac{y}{0}    &    \frac{d}{de} e^x &= xe^{x-1}  \tag{A1} \\[1em]
 \text{eggs} &= \text{bacon}   &  {,} &= {;}   &    7 &= 32  \tag{B1} \\
\end{align*}

\end{document}

Answer 1

If you like to referencing each equation in the system of equation, than see the following solution:

\documentclass{article}
\usepackage{amsmath}
%---------------- show page layout. don't use in a real document!
\usepackage{showframe}
\renewcommand\ShowFrameLinethickness{0.15pt}
\renewcommand*\ShowFrameColor{\color{red}}
%---------------------------------------------------------------%

\begin{document}

\begin{center}
\begin{minipage}{0.3\linewidth}
\begin{align}
 x & = x + 1                    \label{A1}\tag{A1}    \\
 \text{eggs} &= \text{bacon}    \label{B1}\tag{B1}
 \end{align}
\end{minipage}\begin{minipage}{0.3\linewidth}
    \begin{align}
    z   & = \frac{y}{0} \label{A2}\tag{A2}    \\
    {,} & = {;}         \label{B2}\tag{B2}
    \end{align}
    \end{minipage}\begin{minipage}{0.4\linewidth}
        \begin{align}
        \frac{d}{de} e^x & = xe^{x-1}   \label{A3}\tag{A3}    \\
                    7    & = 32         \label{B3}\tag{B3}
        \end{align}
    \end{minipage}
\end{center}
See equations \eqref{A1}, \eqref{B2} and \eqref{A3} \dots
\end{document}

(red lines indicate text area border)