How to align a system of numbered equations

Question

There are solutions to aligning a system unnumbered system of linear equations here: Aligning system of equations with zero coefficients I want a similar solution to numbered system of linear equations. I have also posted a question on using syteme for this here: How to do cross reference in systeme package? However, I find the cross-reference in systeme too painful to use. How to align a system of linear equations with other packages with the standard latex cross reference interface like alignat?

Answer 1

It's fairly straight forward to put a system of linear equations in an alignat if you consider the following basic setup:

• Each alignment point & has a right-&-left (or r&l) alignment structure;

• Keep variables, operators and relations in their own "column";

• Add {} around operators/relations to ensure proper spacing (as in {}+{}, {}-{} and {}={});

• x variables requires x+1 alignment points (so, for 3 variables, you need \begin{alignat}{4}).

In the examples below I've marked the right-alignment point with numbers, which translates to the value used with alignat:

\documentclass{article}

\usepackage{amsmath}

\begin{document}

% 3 variables ~ 4 alignment points
\begin{alignat}{4}
%  1         |  2         |  3         |  4
  2x & {}+{} &  y & {}-{} & 2z & {}={} &  3  \\
   x & {}-{} &  y & {}-{} &  z & {}={} &  0  \\
   x & {}+{} &  y & {}+{} & 3z & {}={} & 12
\end{alignat}

% 3 variables ~ 4 alignment points
\begin{alignat}{4}
%  1         |  2         |  3         |  4
   x &       &    & {}+{} &  z & {}={} &  6  \\
     & {}-{} & 3y & {}+{} &  z & {}={} &  7  \\
  2x & {}+{} &  y & {}+{} & 3z & {}={} & 15
\end{alignat}

% 4 variables ~ 5 alignment points
\begin{alignat}{5}
%   1         |  2         |  3         |  4         |  5
    x & {}+{} &  y & {}+{} &  z & {}+{} &  w & {}={} & 13  \\
   2x & {}+{} & 3y &       &    & {}-{} &  w & {}={} & -1  \\
  -3x & {}+{} & 4y & {}-{} &  z & {}+{} & 2w & {}={} & 10  \\
    x & {}+{} & 2y & {}-{} &  z & {}+{} &  w & {}={} &  1
\end{alignat}

\end{document}

With the above structure in place, you can \label-\ref whatever you need in the usual way.