two possible solution: with array and with matrix extended with solution in
matrix with vertical and horizontal lines :
\documentclass{article}
\usepackage{array}
\usepackage{mathtools}
\makeatletter
\renewcommand*\env@matrix[1][*\c@MaxMatrixCols c]{%
\hskip -\arraycolsep
\let\@ifnextchar\new@ifnextchar
\array{#1}}
\makeatother
\setlength\arraycolsep{1pt}
\begin{document}
\[
\begin{matrix}
(1) \\ (2) \\ (3)
\end{matrix}
\left|\begin{array}{rr rr}
x & y & z & = 33 \\
3x & -8y & +7z & =26 \\
& 5y & -3z & =19
\end{array}\right|
\]
\[
\begin{matrix}
(1) \\ (2) \\ (3)
\end{matrix}
\begin{vmatrix}[rr rr]
x & y & z & = 33 \\
3x & -8y & +7z & =26 \\
& 5y & -3z & =19
\end{vmatrix}
\]
\end{document}
Edit:
As egreg notice, above solution treats + and - as unary rather than as binary operators. For later can be obtained with introduction of new columns for math operators in matrix as well as in array:
\[
\begin{matrix}
(1) \\ (2) \\ (3)
\end{matrix}
\left|\begin{array}{rc rc rr}
x & & y & & z & = 33 \\
3x & - &8y & +& 7z & =26 \\
& &5y & -& 3z & =19
\end{array}\right|
\]
\[
\begin{matrix}
(1) \\ (2) \\ (3)
\end{matrix}
\begin{vmatrix}[rc rc rr]
x & & y & & z & = 33 \\
3x & - &8y & +& 7z & =26 \\
& &5y & -& 3z & =19
\end{vmatrix}
\]

$$...$$to render the content, and the fact that you're only producing math, not just text. MathJax is different from (La)TeX and therefore not entirely supported on this Q&A. – Werner Feb 17 '17 at 17:29