Aligning equations by row and column — with vertical lines

Question

I want to include two sets of equations side-by-side in a table. Here is my example:

\documentclass{article}
\usepackage{amsmath}
\newcommand{\eqnbox}[2]{
  \begin{minipage}[c]{#1\linewidth}\begin{equation*}\begin{aligned}
        #2
      \end{aligned}\end{equation*}\end{minipage}
}
\begin{document}
\begin{center}
\begin{tabular}{c|c}
first set & second set\\
\hline
\eqnbox{.3}{
  x &= \frac{1}{2}\\
  y &= \frac{1}{3}\\
  z &= 3
} &
\eqnbox{.3}{
  x &= 2\\
  y &= 3\\
  z &= 3
}
\end{tabular}
\end{center}
\end{document}

I have tried

1. aligning the rows but putting each equation in $$, but then I cannot align vertically by the = sign.
2. laying out the entire table using align, but then cannot put a vertical line down the middle.
3. adjusting the height of the box by using the height argument to minipage, e.g. \begin{minipage}[c][30pt]{#1\linewidth}, or enclosing the minipage environment within raisebox, e.g., \raisebox{0pt}[30pt][30pt]{}.

No luck so far -- any suggestions?

Answer 1

Use an array instead of the tabular and put the single equations side by side, not the blocks.

\documentclass{article}
\usepackage{amsmath}
\usepackage{array}
\def\MCA#1{\multicolumn{2}{c!{\quad\vline\quad}}{\text{#1}}}
\def\MCB#1{\multicolumn{2}{c}{\text{#1}}}

\begin{document}
\begin{center}
\def\arraystretch{1.8}\arraycolsep=1.4pt
$\begin{array}{rl!{\quad\vline\quad}rl}
\MCA{first set} & \MCB{second set}\\\hline
  x &= \frac{1}{2} &   x &= 2\\
  y &= \frac{1}{3} &   y &= 3\\
  z &= 3           &   z &= 3
\end{array}$
\end{center}

\end{document}