How can I align multiple aligned environments?

Question

I have this equations:

\begin{align}
  \begin{aligned}
    x&=y & z&=w & k&=j \\
    a&=b & c&=d & e&=f \\
  \end{aligned}
  \\
\begin{aligned}
    x+a&=y+b & z+c&=w+d & z+x&=b \\
    a+q&=b+w & c+e&=d+r & e+t&=f+y \\
\end{aligned}
\end{align}

I want all columns to be aligned each others like in the following example:

I have tried to adjust spaces by hands in the following horrible way:

\begin{align}
 x&=y & z&=w & k&=j\nonumber\\[-.25\baselineskip]
 \\[-.75\baselineskip]
 a&=b & c&=d & e&=f
 \nonumber\\
 x+a&=y+b & z+c&=w+d & z+x&=b\nonumber\\[-.25\baselineskip]
 \\[-.75\baselineskip]
 a+q&=b+w & c+e&=d+r & e+t&=f+y\nonumber
\end{align}

Is there a TeXnician solution to do this?

Answer 1

You need to capture the widths of the widest elements in each of your equations. Then you can use those widths to impose alignment between elements that aren't as wide.

Below I use a slight modification to eqparbox via \eqmathbox[<tag>][<align>]{<math>} which stores the maximum width of each <tag>ged box with varying <math> content. Within the box you can change the <align>ment as needed (left, centre or right).

\documentclass{article}

\usepackage{eqparbox,xparse,amsmath}

% https://tex.stackexchange.com/a/34412/5764
\makeatletter
\NewDocumentCommand{\eqmathbox}{o O{c} m}{%
  \IfValueTF{#1}
    {\def\eqmathbox@##1##2{\eqmakebox[#1][#2]{$##1##2$}}}
    {\def\eqmathbox@##1##2{\eqmakebox{$##1##2$}}}
  \mathpalette\eqmathbox@{#3}
}
\makeatother

\begin{document}

\begin{gather}
  \begin{aligned}
    \eqmathbox[ll][r]{x} &= \eqmathbox[lr][l]{y} & 
      \eqmathbox[cl][r]{z} &= \eqmathbox[cr][l]{w} & 
      \eqmathbox[rl][r]{k} &= \eqmathbox[rr][l]{j} \\
    a &= b & c &= d & e &= f \\
  \end{aligned}
  \\
  \begin{aligned}
    x + a &= \eqmathbox[lr]{y + b + c} & 
      \eqmathbox[cl]{z + c + e} &= w + d & 
      z + x &= \eqmathbox[rr]{b + i + j} \\
    \eqmathbox[ll]{a + q + d} &= b + w & 
      c + e &= \eqmathbox[cr]{d + r + o} &
      \eqmathbox[rl]{p + e + t} &= f + y
  \end{aligned}
\end{gather}

\end{document}