Aligning polynomial terms

You could also use the alignat* environment from the amsmath package- see page 5 of the documentation for details and other examples.

Note that without the {} you don't get correct spacing after the + sign.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{alignat*}{4} % 4 is the number of equation columns
  x_1&+x_2&     & =3\\
  x_1&    &{}+x_3 &= 4
\end{alignat*}
\end{document}

EDIT Following mforbes' comment, and a few extra test cases, it is probably more robust to make extra columns for the + and =. For example, say that you wanted to put some coefficients in front of some of the terms.

\begin{alignat*}{4}
     x_1 &{}+{}&x_2    &      &     &{}={}&3\\
     x_1 &     &       &{}+{} & x_3 &{}={}&4
\end{alignat*}

As mforbes pointed out, the amsmath documentation says 'count the maximum number of &s in any row, add 1 and divide by 2'; I've found that if you get a fraction, then you should round up, hence {4} and not {3}.

The systeme package easily enables such alignments:

\documentclass{minimal}
\usepackage{systeme}
\begin{document}
\sysdelim..
\systeme{x_1+x_3=6,x_2-x_3=7,x_1-x_2=4}
\end{document}

Ok, here is my final solution, thanks to everyone's suggestions and guidance. Everything is now clean and well aligned :

\begin{alignat*}
8x_1  &{}+{}&    &4x_2  &{}+{}& y_1                     &&&&&& &{}={}&160\\
4x_1  &{}+{}&    &6x_2  &&       &{}+{}& y_2              &&&& &{}={}&120\\
x_1   &&         &      &&       &&       &{}+{}& y_3       && &{}={}& 34\\
\phantom{{}+{}x_1}
      &&         &x_2   &&       &&          &&    &{}+{}& y_4 &{}={}&14
\end{alignat*}

I've split the inequalities line from the alignat because it was messing with the columns width.

I learned:

• surround the operators in ${}+{}$
• use the exact same number of & on each line
• use \phantom{{}+{}x_1} for missing terms at the head of the polynomial
• don't put anything else (text) in the structure. That will mess thing up
• there are many many ways of doing the same thing and I have a lot to learn

Here's the output: