Fixed Width Font with LTXexample environment

The problem is that the default setting of listings with "fixed columns" has a space 0.6em wide, while the characters in Computer Modern Typewriter are 0.5em wide. So you need only to add the options

columns=fixed,basewidth=.5em,

to \lstset.

One can do without knowing the character width by saying something like

\sbox0{\small\ttfamily A}
\edef\mybasewidth{\the\wd0 }
\lstset{
    basicstyle=\small\ttfamily,% print whole listing small
    columns=fixed,basewidth=\mybasewidth,
    ...}

you should use a good looking typewriterfont like `beramono'

 \documentclass{article}

\usepackage[T1]{fontenc}  
\usepackage[scaled=0.82]{beramono}  
\usepackage{microtype}  
\usepackage{amsmath}  
\usepackage{showexpl} 
\usepackage{xcolor}
\usepackage{multirow} % Newly added for 2nd example.   
\lstset{
     backgroundcolor=\color{yellow},
     basicstyle=\small\ttfamily\SetTracking{encoding=*}{-60}\lsstyle,
     basewidth=0.55em,
     keywordstyle=\color{blue}\bfseries\underbar,
    numbers=left, numberstyle=\tiny, stepnumber=2, numbersep=5pt,
    %columns=fixed,
        %commentstyle=\color{red},
        showstringspaces=false}
    \lstloadlanguages{[LaTeX]TeX}

\begin{document}
Here is an example of LaTeX code and its output:

\begin{LTXexample}[width=0.40\linewidth,preset=\vspace{1.5mm}]
\begin{alignat*}{4}
   y &= -4   &+ 3 &+4     &-7      \\
   y &=      &+ 3 &       &-7      \\
   \intertext{Therefore}
   a &= b    &d   &= cccc &e  &= d \\
   a &= bbbb &d   &= c    &e  &= d
\end{alignat*}
\end{LTXexample}

\begin{LTXexample}[width=0.40\linewidth,preset=\vspace{1.5mm},rframe={},pos=b]
\begin{tabular}{|l|l|l|l|}
\multicolumn{4}{c}{Dimensions} \\
\multirow{4}{*}{Style}
        &\multirow{2}{*}{Portrait} & Width  \\
        &                          & Height \\
        &\multirow{2}{*}{Landscape}& Width  \\
        &                          & Height \\
\end{tabular}
\end{LTXexample}
\end{document}