I would follow the suggestions in the above comments, but just in case you don't want to change your code, you can exploit minipage. Inserting a tabbing inside it causes the minipage to use the width of the tabbing, as egreg suggested in his comments.
MWE
\documentclass{article}
\begin{document}
$ax = b \quad\Leftrightarrow\quad$
\begin{minipage}{\linewidth}
\begin{tabbing}
$a_{11}x_1 + $ \= $a_{12}x_2+\dots +$ \= $a_{1n}x_n$ \= $= b_1$\\
\> $a_{22}x_2 + \dots +$ \> $a_{2n}x_n$ \> $= b_2$\\
\> $\ddots$ \> $\vdots$ \> $\vdots$\\
\> \> $a_{nn}x_n$ \> $= b_n,$
\end{tabbing}
\end{minipage}
\end{document}
Output

The same result can be achieved using the varwidth environment from the same package.
MWE
\documentclass{article}
\usepackage{varwidth}
\begin{document}
$ax = b \quad\Leftrightarrow\quad$
\begin{varwidth}{\linewidth}
\begin{tabbing}
$a_{11}x_1 + $ \= $a_{12}x_2+\dots +$ \= $a_{1n}x_n$ \= $= b_1$\\
\> $a_{22}x_2 + \dots +$ \> $a_{2n}x_n$ \> $= b_2$\\
\> $\ddots$ \> $\vdots$ \> $\vdots$\\
\> \> $a_{nn}x_n$ \> $= b_n,$
\end{tabbing}
\end{varwidth}
\end{document}
alignandarray? Maybe you should read the mathmode. – Marco Daniel Dec 19 '13 at 13:40