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\documentclass[]{article}
\usepackage[utf8]{inputenc}
\usepackage[upright]{fourier}
\usepackage{amsmath,tkz-linknodes}
\thispagestyle{empty}
\begin{document}
% Show how to find the solution of two simultaneous equations.
\begin{minipage}{10cm}
Solution of two simultaneous equations. The problem is to find the set of all solutions that satisfies both equations. These are called simultaneous equations.
\displaywidth=.4\linewidth
\begin{NodesList}[dy=3pt,margin=5cm]
\[ \displaywidth=.4\linewidth
\left\{\begin{matrix}
3x &+& 4y &=& 10\\
2x &+& y &=& 5 \AddNode\\
\end{matrix}\right. \]
\bigskip
\[\displaywidth=.4\linewidth \left\{\begin{matrix}
3x &+& 4y &=& 10\\
8x &+& 4y &=& 20 \AddNode\\
\end{matrix}\right. \]
\bigskip
\[\displaywidth=.4\linewidth \left\{\begin{matrix}
3x &+& 4y &=& 10 \\
5x && &=& 10 \AddNode\\
\end{matrix}\right. \]
\bigskip
\[\displaywidth=.4\linewidth \left\{\begin{matrix}
3(2) &+& 4y &=& 10\\
x && &=& 2 \AddNode\\
\end{matrix}\right. \]
\bigskip
\[\displaywidth=.4\linewidth \left\{\begin{matrix}
3(2) &+& 4y &=& 10\AddNode\\
x && &=& 2 \\
\end{matrix}\right. \]
\bigskip
\[\displaywidth=.4\linewidth \left\{\begin{matrix}
4y &=& 10-6\AddNode\\
x &=& 2 \\
\end{matrix}\right. \]
\bigskip
\[\displaywidth=.4\linewidth \left\{\begin{matrix}
y &=& 1 \AddNode\\
x &=& 2 \\
\end{matrix}\right. \]
\LinkNodes{%
\begin{minipage}{3cm}
both sides of second equation are multiplied by 4
\end{minipage}}
\LinkNodes{%
\begin{minipage}{3cm}
The first equation is subtracted from second
\end{minipage}}
\LinkNodes{$\div 5$}
\LinkNodes{%
\begin{minipage}{3cm}
As a result, $x = 2$, this value is then substituted in the first equation
\end{minipage}}
\LinkNodes{%
\begin{minipage}{3cm}
$6$ is subtracted from both sides
\end{minipage}}
\LinkNodes{$\div 4$}
\end{NodesList}
\end{minipage}
The solution is $\{(x=2~;~y=1)\}$
\end{document}
% Encoding : utf8
% Author : Alain Matthes (2008)
% Engine : pdfLaTeX (LaTeX only with pdftex >= 1.40)
% Packages : xkeyval, tikz with arrow library, amsmath, etex, ifthen
% Remark : needs two compilations
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