Align works well everywhere but at plus sign

Question

I've tried aligning a linear system using this code:

\[\left\{
    \begin{aligned}
        &a_{11}x_1 & + & &a_{12}x_2 & + & &a_{13}x_3 & = & &b_1 \\
        &          &   & &a_{22}x_2 & + & &a_{23}x_3 & = & &b_2 \\
        &          &   & &          &   & &a_{33}x_3 & = & &b_3
    \end{aligned}
        \right.
    \]

Everything works well, except for those two plus signs, as you can see: can someone explain me why?

Answer 1

No additional package is needed.

The root of the issue is the way the columns are align in the aligned structure: rlrlrlr ....

To synchronized the alignment two & are needed before the second + sign

\documentclass{article}

\usepackage{amsmath}
\begin{document}
    
    \[\left\{
    \begin{aligned}
        &a_{11}x_1 & + & &a_{12}x_2 & + & &a_{13}x_3 & = & &b_1 \\
        &          &   & &a_{22}x_2 & + & &a_{23}x_3 & = & &b_2 \\
        &          &   & &          &   & &a_{33}x_3 & = & &b_3
    \end{aligned}
    \right.
    \]
        
    
    \[\left\{
    \begin{aligned}
        &a_{11}x_1 & + & &a_{12}x_2 && + & &a_{13}x_3 & = & &b_1 \\
        &          &   & &a_{22}x_2 && + & &a_{23}x_3 & = & &b_2 \\
        &          &   & &          &&   & &a_{33}x_3 & = & &b_3
    \end{aligned}
    \right. \]

    
\end{document}

See the nice answer align is a table-like structure

Answer 2

Depending on your desired look, you can just align once at the = signs and let the natural math spacing of LaTeX take care of the rest:

\[\left\{
    \begin{aligned}
       a_{11}x_1  + a_{12}x_2  + a_{13}x_3 & = b_1 \\
       a_{22}x_2  + a_{23}x_3 & = b_2 \\
       a_{33}x_3 &= b_3
    \end{aligned}
\right.\]

Answer 3

I have worked out a solution with the array package.

\documentclass{scrarticle}

\usepackage{amsmath}
\usepackage{array}

\begin{document}
    \begin{equation*}
        \left\{
        \begin{array}{ccccccc}
            a_{11}x_{1} & + & a_{12}x_{2} & + & a_{13}x_{3} & = & b_1 \\ 
            & & a_{22}x_{2} & + & a_{23}x_{3} & = & b_2 \\
            & & & & a_{33}x_{3} & = & b_3
        \end{array}
        \right.
    \end{equation*}
\end{document}

The output looks like this If you insist on doing it with the aligned environment, this is no solution for you. But like you I often struggled with it and someone on here suggested the array package and I liked it, maybe you will too.

Answer 4

You can use alignedat instead, or \systeme.

\documentclass{article}
\usepackage{amsmath}
\usepackage{systeme}% for the second solution

\begin{document}

\[
\left\{
\begin{alignedat}{3}
  a_{11}x_1 & +{} & a_{12}x_2 & +{} & a_{13}x_3 & = b_1 \\
            &     & a_{22}x_2 & +{} & a_{23}x_3 & = b_2 \\
            &     &           &     & a_{33}x_3 & = b_3
\end{alignedat}
\right.
\]

\[
\syssubstitute{{A}{a_{11}}{B}{a_{12}}{C}{a_{13}}{D}{a_{22}}{E}{a_{23}}{F}{a_{33}}}
\systeme{
  Ax_1 + Bx_2 + Cx_3 = b_1,
         Dx_2 + Ex_3 = b_2,
                Fx_3 = b_3
}
\]

\end{document}

Answer 5

Here is a solution using the IEEEeqnarraybox environment from the IEEEtrantools (Appendix F of the documentation) package. This tutorial on typesetting equations also demonstrates the usage of the IEEEeqnarray environment.

\documentclass{article}

\usepackage{IEEEtrantools}

\begin{document}
\[
\left\{
\begin{IEEEeqnarraybox}[\relax][c]{;r'r'r'r'r'C'l}
a_{11}x_1 &+& a_{12}x_2 &+& a_{13}x_3 &=& b_1 \\
          & & a_{22}x_2 &+& a_{23}x_3 &=& b_2 \\
          & &           & & a_{33}x_3 &=& b_3
\IEEEstrut
\end{IEEEeqnarraybox}
\right.
\]
\end{document}

The separation between columns can be changed by using different glue types. Here I have used the ; glue (inserts 5/18em space) between the { and the 1st column and ' glue (inserts 1em space) between other columns. For other glue types, please refer to the documentation.

Answer 6

As @daleif comments, the problem could be solved easily by add a {} before & which could protect the space around symbols near &. By the way the codes could be simplified and rewritten as follows:

\[\left\{
    \begin{aligned}
        a_{11}x_1 + a_{12}x_2  + {}&a_{13}x_3  = b_1 \\
                 a_{22}x_2  + {}&a_{23}x_3  = b_2 \\
                 {}&a_{33}x_3  = b_3
    \end{aligned}
\right.\]