Space in array system equations
You can better exploit array
:
\documentclass{article}
\usepackage{amsmath,array,cancel}
\newenvironment{system}[1]
{%
\left|\setlength{\arraycolsep}{0pt}
\begin{array}{ @{} *{\numexpr2*#1\relax}{ >{{}} r <{{}} } l @{} }%
}
{\end{array}\right.}
\begin{document}
$\begin{system}{3}
2x &+& 3y &-& \cancel{z} &=& 4 \\
3x &+& 2y &+& \cancel{z} &=& 6
\end{system}
\rightarrow
5x+5y=10
\rightarrow
x+y=2
\rightarrow
\begin{system}{3}
x &-& y &+& 2z &=& 2 \\
3x &+& 2y &-& z &=&4 \mid .2
\end{system}$
\end{document}
This way the unknowns are perfectly aligned to each other. The argument to system
specifies the number of unknowns.
Rather than eliminating the space, I propose working instead to align columns in the systems of equations. Also, by making it one big math expression, the spacing also takes on a more natural appearance.
\documentclass{article}
\usepackage{array,amsmath,cancel,tabstackengine}
\setstacktabulargap{0pt}
\TABstackMath
\begin{document}
\noindent Example 1:
\\
$\left| \tabularCenterstack{rrrl}{
2x+&3y-&\cancel{z}=&4 \\
3x+&2y+&\cancel{z}=&6
}\right.
\rightarrow
5x+5y=10 \rightarrow
x+y=2;
\left| \tabularCenterstack{rrrl}{
x-&y+&2z=&2 \\
3x+&2y-&z=&4 | .2
}\right.
\rightarrow$
\end{document}
It is quite simple to type it with the systeme
package:
\documentclass{article}
\usepackage{amsmath, cancel, systeme}
\begin{document}
\[ \sysdelim | .
\systeme{2x + 3y-\cancel z = 4,3x + 2y + z = 6} \longrightarrow 5x + 5y = 10 \longrightarrow x + y = 20 \longrightarrow \systeme{x-y + 2z = 2, 3x + 2y - z = 4|. 2} \]%
\end{document}