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\begin{document}

\title{AP 11 -- Solve a system by elimination}
\subtitle{European section, season 01}
\date{}

\begin{frame}
  \titlepage
\end{frame}


\begin{frame}{The game}

\Large

There are three type of coloured cards : green, yellow and blue. 

\bigskip

Each blue card has a value of 1, but the values of the green and yellow cards are unknown. 

\bigskip

You have to find them by solving a system made of two sentences.

\end{frame}

\begin{frame}{An example}

\large

$$\left\{
\begin{array}{l}
\text{Two green cards and two yellow cards make four.}\\
\text{Three green cards and one yellow card make four.}
\end{array}\right.$$

\end{frame}

\begin{frame}{Step 1 : Set up the two equations.}
 
\begin{center}
\includegraphics[scale=0.18]{images/step0big.eps}
\end{center}

\end{frame}

\begin{frame}{Step 2 : Multiply one equation so that the number of yellow (or green) cards are equal.}

\begin{center}
\includegraphics[scale=0.18]{images/step1big.eps}
\end{center}

Note : You may need to multiply both equations.
\end{frame}

\begin{frame}{Step 3 : Take from each equation the number of green, yellow and blue cards there are in one of the equations.}

\begin{center}
\includegraphics[scale=0.22]{images/step2big.eps}
\end{center}


\end{frame}

\begin{frame}{Step 4 : Deduce the value of the green card.}

\begin{center}
\includegraphics[scale=0.3]{images/step3big.eps}
\end{center}

\end{frame}

\begin{frame}{Step 5 : Go back to the first equation.}

\begin{center}
\includegraphics[scale=0.3]{images/step4big.eps}
\end{center}

\end{frame}

\begin{frame}{Step 6 : Replace each green card by the appropriate number of blue cards.}

\begin{center}
\includegraphics[scale=0.3]{images/step5big.eps}
\end{center}

\end{frame}

\begin{frame}{Step 7 : Subtract the same number of blue cards from both sides.}

\begin{center}
\includegraphics[scale=0.3]{images/step6big.eps}
\end{center}

\end{frame}

\begin{frame}{Step 8 : Deduce the value of the yellow card.}


\begin{center}
\includegraphics[scale=0.3]{images/step7big.eps}
\end{center}

\end{frame}

\begin{frame}{Step 9 : Conclude}

\Large 

\begin{center}
The values of the green and yellow cards are both equal to 1.
\end{center}



\end{frame}




\end{document}
