Spacing and triple alignment within cases

Question

I am struggling regarding the alignment and spacing of the numbers within the cases. For alignment I usually use arrays but those don't seem to work within cases. The questions and answers I found here were only regarding one alignment where the & would work with arrays. But I have multiple alignments, and multiple &'s don't work within a case.

I now use the systeme package, but that package is not really stable. Especially when using brackets and letters. Also spacing is an issue within the current solution, as seen on the right. The numbers are pretty close together. I also tried things like \quad but pretty much always the case breaks because of the alpha's

\systeme{
  x_1       +         2x_2       +              2 x_3       =       \alpha,
                       x_2                                  =       \alpha,
 2x_1       +         3x_2       +         \alpha x_3       =       0}

While my current work (below one) is acceptable, I rather have the spacing the upper one has. It looks a lot better. Does anyone have a method how to achieve the alignment of the upper one? I rather not use the systeme package if that's possible.

Answer 1

Here is a solution using the IEEEeqnarraybox environment from the IEEEtrantools package. The ; glue defines 5/18 em and the ' glue defines 1 em separation between columns.

\documentclass{article}

\usepackage{IEEEtrantools}

\begin{document}
\[
\left\{
\begin{IEEEeqnarraybox}[\relax][c]{;r'r'r'r'r'C'l}
      x_1       &+&         2x_2       &+&              2 x_3       &=&       \alpha,\\
                & &         x_2        & &                          &=&       \alpha,\\
     2x_1       &+&         3x_2       &+&         \alpha x_3       &=&       0
\end{IEEEeqnarraybox}
\right.
\]
\end{document}

Answer 2

The solution is explained in § 1.9, Espaces autour des signes, p.6 in the documentation:

\documentclass{article}
\usepackage{systeme}

\begin{document}

\syssignspace{0.5em}\syseqspace{0.5em}
\systeme{
  x_1 + 2x_2 + 2 x_3 = \alpha,
                       x_2 = \alpha,
 2x_1 + 3x_2 + \alpha x_3 = 0}

\end{document}