How to align math equations even when some variables are missing?

Question

I want the variables and signs aligned in a set of equations.

Desired output:

What I am trying in Mathjax:

\[
\begin{align}
2&x_1 - x_2 &+ 1.5&x_3 &= 8 \\
&x_1 &- 4&x_3 &= -1
\end{align}
\]

What I got:

So, what do I have to do to have the same alignment as in the "desired output" image?

Answer 1

There are a number of ways to achieve this. Below I use an array (with appropriate stretch and spacing), alignat and align coupled with eqparbox for measuring similarly-tagged boxes (this latter approach requires two compilations with every change in the largest element associated with every <tag>):

\documentclass{article}

\usepackage{amsmath,eqparbox}

%\usepackage{xparse}% If you have LaTeX2e < 2020-10-01

% https://tex.stackexchange.com/a/34412/5764
\makeatletter
% \eqmathbox[<tag>][<align>]{<math>}
\NewDocumentCommand{\eqmathbox}{o O{c} m}{%
  \IfValueTF{#1}
    {\def\eqmathbox@##1##2{\eqmakebox[#1][#2]{$##1##2$}}}
    {\def\eqmathbox@##1##2{\eqmakebox{$##1##2$}}}
  \mathpalette\eqmathbox@{#3}
}
\makeatother


\begin{document}

\[
  \renewcommand{\arraystretch}{1.2}
  \setlength{\arraycolsep}{0pt}
  \begin{array}{ r c r c r c r }
    2 x_1 & {}-{} & x_2 & {}+{} & 1.5 x_3 & {}={} &  8 \\
      x_1 &       &     & {}-{} &   4 x_3 & {}={} & -7
  \end{array}
\]

\begin{alignat*}{4}
  2 x_1 & {}-{} & x_2 & {}+{} & 1.5 x_3 = {} &&  8 \\
    x_1 &       &     & {}-{} &   4 x_3 = {} && -7
\end{alignat*}

\begin{align*}
  \eqmathbox[x1][r]{2 x_1}         -       \eqmathbox[x2][r]{x_2} + \eqmathbox[x3][r]{1.5 x_3} &= \eqmathbox[c][r]{8} \\
  \eqmathbox[x1][r]{  x_1} \phantom{{}-{}} \eqmathbox[x2][r]{} - \eqmathbox[x3][r]{4 x_3} &= \eqmathbox[c][r]{-7}
\end{align*}

\end{document}

All yield similar output: