Two sets of aligned equations in two columns?

Question

Say I have a set of equations:

(1)

\begin{align}
wx&=u\\
wy&=v\\
w&=10
\end{align}

(2)

\begin{align}
x&=u/w\\
y&=v/w\\
\end{align}

How can I do the following: put (1) and (2) in the same line but in two separate columns, and add a \leftrightarrow between them? i.e., something like

I tried putting (1) (2) and arrow in three minipage environments, but the width of minipage is hard to tune when (1) (2) have different width and looks quite ugly as above.

Answer 1

Try the aligned environment from the amsmath package.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation*}
\begin{aligned}[c]
wx&=u\\
wy&=v\\
w&=10
\end{aligned}
\qquad\Longleftrightarrow\qquad
\begin{aligned}[c]
x&=u/w\\
y&=v/w\\
\end{aligned}
\end{equation*}
\end{document}

Answer 2

Also from the amsmath package, and closely related to Ian Thompson's answer, is one using the split environment:

\begin{equation}
  \begin{split}
    wu &= ax+by+c\\
    wv &= dx+ey+f\\
    w &= gx+hy+i
  \end{split}
\quad\leftrightarrow\quad
  \begin{split}
    ax+by+c-xug-uyh-ui &= 0\\
    dx+ey+f-xvg-yvh-vi &= 0
  \end{split}
\end{equation}

Answer 3

For the sake of completeness, and perhaps an educative measure in terms of boxing (since the OP mentioned it), here's some minipage usage:

\documentclass{article}
\begin{document}
Here is some preceding text:
\[
\begin{minipage}{.35\linewidth}
  \centering
  $\begin{array}{r@{{}\mathrel{=}{}}l}
    wx & u \\[\jot]
    wy & v \\[\jot]
    w  & 10
  \end{array}$
\end{minipage}%
\begin{minipage}{.3\linewidth}
\centering (1)~$\leftrightarrow$~(2)
\end{minipage}%
\begin{minipage}{.35\linewidth}
  \centering
  $\begin{array}{r@{{}\mathrel{=}{}}l}
    x & u/w \\[\jot]
    y & v/w
  \end{array}$
\end{minipage}
\]
Here is some text following the above boxed expression.
\end{document}

Note that the minipage widths sum to \linewidth and are evenly distributed across it. The use of arrays just make the vertical alignment easier.

If you're interested in seeing the boxes used in the above construction, wrap each minipage inside an \fbox (after setting \setlength{\fboxsep}{-\fboxrule} to avoid changes when visualizing the boxes):