Two equations on the same line

Question

I have seen some posts close to what I need, but not quite what I need.

I would like to produce two equations on the same line with one equation number adjusted to left and one to the right. Both equations should be multiline.

And I want to generate a \tag for both equation labels.

So the output should look like what is produced by the code below.

\begin{array}{llrr}
      &    a=b                  &      x=y    &   \\
(eq1) &    c=d                  &      y=z    & (eq2)     \\
      &    e=f                 &       u=v
\end{array}

Answer 1

I propose this solution, with a code borrowed on this site from @DavidCarlisle:

\documentclass{article}
\usepackage[utf8]{inputenc}%
\usepackage{tabularx} 
\usepackage{mathtools, nccmath}

\makeatletter
\newcommand{\leqnomode}{\tagsleft@true\let\veqno\@@leqno}%
\newcommand{\reqnomode}{\tagsleft@false\let\veqno\@@eqno}%
\newcommand*{\compress}{\@minipagetrue}
\makeatother

\begin{document}

Some text. Some text. Some text. Some text. Some text. Some text. Some text. Some text. Some text. Some text. Some text. Some text. Some text. Some text. Some text. Some text.

{\centering\compress
\begin{tabularx}{\linewidth}{>{\leqnomode}XX}
\begin{equation}
\begin{aligned}
       a & =b \\
    c & =d \\
       e & =f
\end{aligned}
\end{equation}
 &
 \begin{equation}
\begin{aligned}
x & =y \\
 y & =z \\
u & =v
\end{aligned}
\end{equation}
\end{tabularx} \vspace{-\baselineskip}}

 Some more text. Some more text. Some more text. Some more text. Some more text. Some more text. Some more text. Some more text.

\end{document} 

Answer 2

Like this:

\documentclass{article}
\usepackage{tabularx}
\newcolumntype{C}{>{\centering\arraybackslash}X}
\usepackage{amsmath}

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

\begin{document}
\lipsum*[66]
    \begin{center}
    \begin{tabularx}{\linewidth}{@{} lCCr @{}}
\refstepcounter{equation}
(\theequation)\label{eq:left}
    &   $\begin{aligned}
        a & = b \\
        c & = d
        \end{aligned}$
        &   $\begin{aligned}
            x & = y \\
            z & = w
            \end{aligned}$
            &   \refstepcounter{equation}
                (\theequation)\label{eq:right}
    \end{tabularx}
    \end{center}
\dots, see \eqref{eq:left} and \eqref{eq:right} \dots
\lipsum*[66]
\end{document}

Addendum: I figured out how to use my own tags for equations:

\documentclass{article}

\usepackage{amsmath}
\makeatletter
\newcommand{\leqnomode}{\tagsleft@true}
\newcommand{\reqnomode}{\tagsleft@false}
\makeatother

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

\begin{document}
\lipsum*[66]
    \begin{center}
    \vspace{-\baselineskip}
    \begin{minipage}{0.5\linewidth}\leqnomode
\begin{equation}\label{eq:left}
\begin{split}
        a & = b \\
        c & = d
\end{split}\tag{*}
\end{equation}
\end{minipage}\begin{minipage}{0.5\linewidth}
\begin{equation}\label{eq:right}
\begin{split}
        x & = y \\
        z & = uvw
\end{split}\tag{**}
\end{equation}
    \end{minipage}
    \end{center}
\dots, see \eqref{eq:left} and \eqref{eq:right} \dots
\lipsum*[66]
\end{document}

Answer 3

I'm not sure it is a good idea.

\documentclass{article}
\usepackage{amsmath}
\usepackage{array}
\usepackage{lipsum} % for context

\newenvironment{doublynumberedequation}[2]
 {%
  \unskip
  \refstepcounter{equation}\label{#1}%
  \refstepcounter{equation}\label{#2}%
  \def\secondlabel{#2}%
  \begin{equation*}
  \begin{tabular*}{\displaywidth}{
    @{\extracolsep{\stretch{1}}}
    l
    >{$\displaystyle}c<{$}
    @{\extracolsep{\stretch{2}}}
    >{$\displaystyle}c<{$}
    @{\extracolsep{\stretch{1}}}
    r
    @{}
  }
  \eqref{#1} &
 }
 {& \eqref{\secondlabel}\end{tabular*}\end{equation*}}

\begin{document}

\lipsum*[4]
\begin{doublynumberedequation}{left}{right}% use two meaningful labels
  \begin{aligned}
  a&=b \\
  c&=d \\
  e&=f
  \end{aligned}
&
  \begin{aligned}
  x&=y \\
  y&=z \\
  u&=v
  \end{aligned}
\end{doublynumberedequation}
\lipsum[5]

\end{document}