As @vonbrand said, you can easily write systems of equations using systeme package, sadly for me the documentation is in french.
Code:
\documentclass{article}
\usepackage{systeme}
\begin{document}
\systeme{3x+2y-5z=4,2x+4y-z=12,-4x-8y+9z=-6}%Default settings
\medskip
\sysdelim{.}{.}\systeme{3x+2y-5z=4,2x+4y-z=12,-4x-8y+9z=-6}%Without the left brace
\medskip
\sysdelim{.}{.}\systeme{3x+2y-5z=4@E_{*},2x+4y-z=12,-4x-8y+9z=-6}%Equations with numbers
\end{document}
Output

UPDATE
This question shows you how to the change the alignment of the RHS of the equations in order to do that you just need to redefine the command \SYS@makesyspreamble@i as @egreg mentioned
UPDATE Code
\documentclass{article}
\usepackage{systeme}
\usepackage{regexpatch}
\makeatletter
\xpatchcmd{\SYS@makesyspreamble@i}
{$##$\hfil\null}% left alignment
{\hfil$##$\null}% right alignment
{}{}
\makeatother
\begin{document}
\systeme{3x+2y-5z=4,2x+4y-z=12,-4x-8y+9z=-6}
\medskip
\sysdelim{.}{.}\systeme{3x+2y-5z=4,2x+4y-z=12,-4x-8y+9z=-6}
\medskip
\sysdelim{.}{.}\systeme{3x+2y-5z=4@E_{*},2x+4y-z=12,-4x-8y+9z=-6}
\end{document}