The systeme package does this in a very pretty way:
\documentclass{article}
\usepackage{amsmath}
\usepackage{systeme}
\begin{document}
\[
\systeme{
x_{1} - 3x_{2} + 4x_{3} = -4,
3x_{1} - 7x_{2} + 7x_{3} = -8,
-4x_{1} + 6x_{2} - x_{3} = 7
}
\]
\end{document}

If you search on the site for systeme, you'll find several other examples.
For instance, in order to have the constant terms flush right, you can look at Is it possible to flushright the right-hand side with systeme without \hphantom?
\documentclass{article}
\usepackage{amsmath}
\usepackage{systeme}
\usepackage{regexpatch}
\makeatletter
\xpatchcmd{\SYS@makesyspreamble@i}
{$##$\hfil\null}% left alignment
{\hfil$##$\null}% right alignment
{}{}
\makeatother
\begin{document}
\[
\systeme{
x_{1} - 3x_{2} + 4x_{3} = -4,
3x_{1} - 7x_{2} + 7x_{3} = -8,
-4x_{1} + 6x_{2} - x_{3} = 7
}
\]
\end{document}

\phantom{-}7. – Werner Feb 03 '16 at 22:42systemein the site gives an answer. – egreg Feb 03 '16 at 22:43\sysdelim{.}{.}in the preamble; or you can do it locally by placing the same command between\[(or\begin{equation}) and\systeme; in this case it will hold only for the next system. – egreg Feb 03 '16 at 22:52