Here's a LyX file (including step by step instructions).

Paul

#LyX 2.0 created this file. For more info see http://www.lyx.org/
\lyxformat 413
\begin_document
\begin_header
\textclass article
\use_default_options true
\maintain_unincluded_children false
\language english
\language_package default
\inputencoding auto
\fontencoding global
\font_roman lmodern
\font_sans lmss
\font_typewriter lmtt
\font_default_family default
\use_non_tex_fonts false
\font_sc false
\font_osf false
\font_sf_scale 100
\font_tt_scale 100

\graphics default
\default_output_format default
\output_sync 0
\bibtex_command default
\index_command default
\paperfontsize default
\spacing single
\use_hyperref false
\papersize letterpaper
\use_geometry true
\use_amsmath 1
\use_esint 1
\use_mhchem 1
\use_mathdots 1
\cite_engine basic
\use_bibtopic false
\use_indices false
\paperorientation portrait
\suppress_date false
\use_refstyle 0
\index Index
\shortcut idx
\color #008000
\end_index
\leftmargin 1in
\topmargin 1in
\rightmargin 1in
\bottommargin 1in
\secnumdepth 3
\tocdepth 3
\paragraph_separation skip
\defskip medskip
\quotes_language english
\papercolumns 1
\papersides 1
\paperpagestyle default
\tracking_changes false
\output_changes false
\html_math_output 0
\html_css_as_file 0
\html_be_strict false
\end_header

\begin_body

\begin_layout Standard
\begin_inset Formula 
\[
\textrm{System: }\begin{aligned}2x-3y=8\\
4x+5y=1
\end{aligned}
\qquad\textrm{Augmented Matrix: }\left[\begin{array}{cc|c}
2 & -3 & 8\\
4 & 5 & 1
\end{array}\right]
\]

\end_inset


\end_layout

\begin_layout Standard
Construction:
\end_layout

\begin_layout Enumerate
Insert > Math > Display Formula
\end_layout

\begin_layout Enumerate
Type 
\backslash
textrm (space) to create text insert
\end_layout

\begin_deeper
\begin_layout Enumerate
Type 
\begin_inset Quotes eld
\end_inset

System: 
\begin_inset Quotes erd
\end_inset

 (including the space)
\end_layout

\begin_layout Enumerate
Exit the text inset (staying inside the formula inset) using the cursor
 keys or mouse
\end_layout

\end_deeper
\begin_layout Enumerate
Type 
\backslash
aligned (space) to create an aligned inset
\end_layout

\begin_deeper
\begin_layout Enumerate
Type the first equation and hit Ctrl-Enter to get a second line
\end_layout

\begin_layout Enumerate
Type the second equation and exit the aligned inset using the arrow key,
 space key or mouse
\end_layout

\end_deeper
\begin_layout Enumerate
Type Ctrl-Space and add a few more spaces to separate the two parts
\end_layout

\begin_layout Enumerate
Repeat step 2 using the text 
\begin_inset Quotes eld
\end_inset

Augmented Matrix: 
\begin_inset Quotes erd
\end_inset


\end_layout

\begin_layout Enumerate
Use Insert > Math > Delimiters to create the brackets for the matrix
\end_layout

\begin_layout Enumerate
Use Insert > Math > Array Environment to create a 2x3 array
\end_layout

\begin_deeper
\begin_layout Enumerate
Enter the coefficients
\end_layout

\begin_layout Enumerate
With the cursor in the last column (either row), click Edit > Math > Add
 Line to Left
\end_layout

\end_deeper
\begin_layout Standard

\end_layout

\end_body
\end_document



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