\documentclass[12pt]{article}\usepackage{ammaths}\en

\begin{document}

\module{Solving a system graphically}{01}{AP12}{55 mins}

\prereq{Solve a system by elimination. Line equations.}

\object{\begin{itemize}
        \item Practise the graphical method for solving a system.
	\end{itemize}}

\mater{\begin{itemize}
	\item Answer sheets.
	\item Graphed tracing paper.
	\item Line equations.
	\item Slideshow.
	\end{itemize}}

\modpart{Find the other half of your system}{10 mins}

\begin{enumerate}
\item Each student is given a line equation and has to draw the line on a sheet of graphed tracing paper. It's important
that everyone uses exactly the same units, and better if they place the axes in the same position.
\item A list of coordinate couples (9 or 10) is projected on the board.
\item Each student has to find another one such that the solution of the system made by their two equations is one of
the coordinates.
\item Once a pair is formed, the two students have to solve the system algebraically to check the solution.
\end{enumerate}

\modpart{System solving contest}{45 mins}

Students work by pairs. Each pair has to find graphically an approximate solution of the system made by their two
equations, then check the answer algebraically. Then, they move on to make other pairs with other students.

Students get a mark at the end of the session, depending on the number of systems they correctly solved.

\pagebreak

\moddocdis{Solving a system graphically}{01}{AP12}{Answer sheet}

\newcounter{sys}
\newcommand{\sys}{\stepcounter{sys}\arabic{sys}}

\subsection*{System \sys}

\begin{tabular}{cp{0.5cm}cp{0.5cm}c}
System && Approximate solution && Exact solution \\
\cline{3-3}\cline{5-5}
$\left\{\begin{array}{l}
\underline{\text{\rule{5cm}{0pt}\rule{0pt}{25pt}}} \\
\underline{\text{\rule{5cm}{0pt}\rule{0pt}{25pt}}} \\
\end{array}\right.$ &&
\multicolumn{1}{|c|}{\rule{4cm}{0pt}} && \multicolumn{1}{|c|}{\rule{2.75cm}{0pt}}\\
\cline{3-3}\cline{5-5}
\end{tabular}


\subsection*{System \sys}

\begin{tabular}{cp{0.5cm}cp{0.5cm}c}
System && Approximate solution && Exact solution \\
\cline{3-3}\cline{5-5}
$\left\{\begin{array}{l}
\underline{\text{\rule{5cm}{0pt}\rule{0pt}{25pt}}} \\
\underline{\text{\rule{5cm}{0pt}\rule{0pt}{25pt}}} \\
\end{array}\right.$ &&
\multicolumn{1}{|c|}{\rule{4cm}{0pt}} && \multicolumn{1}{|c|}{\rule{2.75cm}{0pt}}\\
\cline{3-3}\cline{5-5}
\end{tabular}

\subsection*{System \sys}

\begin{tabular}{cp{0.5cm}cp{0.5cm}c}
System && Approximate solution && Exact solution \\
\cline{3-3}\cline{5-5}
$\left\{\begin{array}{l}
\underline{\text{\rule{5cm}{0pt}\rule{0pt}{25pt}}} \\
\underline{\text{\rule{5cm}{0pt}\rule{0pt}{25pt}}} \\
\end{array}\right.$ &&
\multicolumn{1}{|c|}{\rule{4cm}{0pt}} && \multicolumn{1}{|c|}{\rule{2.75cm}{0pt}}\\
\cline{3-3}\cline{5-5}
\end{tabular}

\subsection*{System \sys}

\begin{tabular}{cp{0.5cm}cp{0.5cm}c}
System && Approximate solution && Exact solution \\
\cline{3-3}\cline{5-5}
$\left\{\begin{array}{l}
\underline{\text{\rule{5cm}{0pt}\rule{0pt}{25pt}}} \\
\underline{\text{\rule{5cm}{0pt}\rule{0pt}{25pt}}} \\
\end{array}\right.$ &&
\multicolumn{1}{|c|}{\rule{4cm}{0pt}} && \multicolumn{1}{|c|}{\rule{2.75cm}{0pt}}\\
\cline{3-3}\cline{5-5}
\end{tabular}

\subsection*{System \sys}

\begin{tabular}{cp{0.5cm}cp{0.5cm}c}
System && Approximate solution && Exact solution \\
\cline{3-3}\cline{5-5}
$\left\{\begin{array}{l}
\underline{\text{\rule{5cm}{0pt}\rule{0pt}{25pt}}} \\
\underline{\text{\rule{5cm}{0pt}\rule{0pt}{25pt}}} \\
\end{array}\right.$ &&
\multicolumn{1}{|c|}{\rule{4cm}{0pt}} && \multicolumn{1}{|c|}{\rule{2.75cm}{0pt}}\\
\cline{3-3}\cline{5-5}
\end{tabular}

\subsection*{System \sys}

\begin{tabular}{cp{0.5cm}cp{0.5cm}c}
System && Approximate solution && Exact solution \\
\cline{3-3}\cline{5-5}
$\left\{\begin{array}{l}
\underline{\text{\rule{5cm}{0pt}\rule{0pt}{25pt}}} \\
\underline{\text{\rule{5cm}{0pt}\rule{0pt}{25pt}}} \\
\end{array}\right.$ &&
\multicolumn{1}{|c|}{\rule{4cm}{0pt}} && \multicolumn{1}{|c|}{\rule{2.75cm}{0pt}}\\
\cline{3-3}\cline{5-5}
\end{tabular}

\subsection*{System \sys}

\begin{tabular}{cp{0.5cm}cp{0.5cm}c}
System && Approximate solution && Exact solution \\
\cline{3-3}\cline{5-5}
$\left\{\begin{array}{l}
\underline{\text{\rule{5cm}{0pt}\rule{0pt}{25pt}}} \\
\underline{\text{\rule{5cm}{0pt}\rule{0pt}{25pt}}} \\
\end{array}\right.$ &&
\multicolumn{1}{|c|}{\rule{4cm}{0pt}} && \multicolumn{1}{|c|}{\rule{2.75cm}{0pt}}\\
\cline{3-3}\cline{5-5}
\end{tabular}

\subsection*{System \sys}

\begin{tabular}{cp{0.5cm}cp{0.5cm}c}
System && Approximate solution && Exact solution \\
\cline{3-3}\cline{5-5}
$\left\{\begin{array}{l}
\underline{\text{\rule{5cm}{0pt}\rule{0pt}{25pt}}} \\
\underline{\text{\rule{5cm}{0pt}\rule{0pt}{25pt}}} \\
\end{array}\right.$ &&
\multicolumn{1}{|c|}{\rule{4cm}{0pt}} && \multicolumn{1}{|c|}{\rule{2.75cm}{0pt}}\\
\cline{3-3}\cline{5-5}
\end{tabular}

\subsection*{System \sys}

\begin{tabular}{cp{0.5cm}cp{0.5cm}c}
System && Approximate solution && Exact solution \\
\cline{3-3}\cline{5-5}
$\left\{\begin{array}{l}
\underline{\text{\rule{5cm}{0pt}\rule{0pt}{25pt}}} \\
\underline{\text{\rule{5cm}{0pt}\rule{0pt}{25pt}}} \\
\end{array}\right.$ &&
\multicolumn{1}{|c|}{\rule{4cm}{0pt}} && \multicolumn{1}{|c|}{\rule{2.75cm}{0pt}}\\
\cline{3-3}\cline{5-5}
\end{tabular}

\subsection*{System \sys}

\begin{tabular}{cp{0.5cm}cp{0.5cm}c}
System && Approximate solution && Exact solution \\
\cline{3-3}\cline{5-5}
$\left\{\begin{array}{l}
\underline{\text{\rule{5cm}{0pt}\rule{0pt}{25pt}}} \\
\underline{\text{\rule{5cm}{0pt}\rule{0pt}{25pt}}} \\
\end{array}\right.$ &&
\multicolumn{1}{|c|}{\rule{4cm}{0pt}} && \multicolumn{1}{|c|}{\rule{2.75cm}{0pt}}\\
\cline{3-3}\cline{5-5}
\end{tabular}






\pagebreak

\moddoc{Line equations}

\huge

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$$x-2y=-9$$ 

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$$2x+y=-8$$

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$$x+y=1$$

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$$-2x+y=7$$

\bigskip
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$$2x-y=0$$

\bigskip
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$$x+y=6$$

\bigskip
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$$2x+y=15$$

\bigskip
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$$-2x+y=-9$$

\bigskip
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$$x+5y=-4$$

\bigskip
\hrule
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$$x-y=8$$

\bigskip
\hrule

\pagebreak

\hrule
\bigskip

$$3x-2y=7$$

\bigskip
\hrule
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$$x+2y=5$$

\bigskip
\hrule
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$$x+y=-4$$

\bigskip
\hrule
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$$5x-2y=-6$$

\bigskip
\hrule
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$$3x+2y=-20$$

\bigskip
\hrule
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$$-2x+5y=7$$

\bigskip
\hrule
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$$x-6y=30$$

\bigskip
\hrule
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$$3x+y=-5$$

\bigskip
\hrule
\bigskip

$$7x+y=10$$

\bigskip
\hrule
\bigskip

$$-3x+4y=-22$$

\bigskip
\hrule
\bigskip







\end{document}
