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%TCIDATA{<META NAME="Title" CONTENT="Elimination">}
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\lhead{\color{blue} \Large Math 99}
\chead{\color{black} \LARGE Linear Systems  - Elimination}
\rhead{\large }
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\lfoot{\small   \copyright $\;$ copyright  Hidegkuti,  Powell,  2011}
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\begin{document}


\begin{enumerate}
\item Solve each of the following system of linear equations by elimination.$%
\medskip $

a) \ $\left\{ 
\begin{array}{c}
3x+y=5 \\ 
2x-y=15%
\end{array}%
\right. $ \ \ \ \ \ \ c) \ $\left\{ 
\begin{array}{c}
3x+y=10 \\ 
5x-y=-2%
\end{array}%
\right. $ \ \ \ \ \ \ \ e) \ $\left\{ 
\begin{array}{c}
-2x+3y=-11 \\ 
5x-2y=0%
\end{array}%
\right. \medskip $

b) $\ \left\{ 
\begin{array}{c}
x+5y=32 \\ 
x-2y=-24%
\end{array}%
\right. $ \ \ \ \ \ \ d) $\ \left\{ 
\begin{array}{c}
4x+5y=12 \\ 
-3x+y=-9%
\end{array}%
\right. $ \ \ \ \ \ \ \ f) \ $\left\{ 
\begin{array}{c}
4x-5y=30 \\ 
7x+2y=-12%
\end{array}%
\right. \medskip \medskip $

\item There is an animal farm where chickens and cows live. \ All together,
there are $53$ heads and $174$ legs. \ How many chickens and how many cows
are there on the farm?$\medskip $

\item The sum of two numbers is $73$, their difference is $29$. \ Find these
numbers.$\medskip $

\item We have some $\$10$ dollar bills and some $\$20$ dollar bills. \ How
many of each do we have if all together, we have $42$ bills and their total
value is $\$620$? $\medskip $

\item We have some coins, all dimes and quarters. \ How many of each type of
coins do we have if all together, we have $83$ coins and their total value
is $\$15.50$?
\end{enumerate}

\pagebreak 

\begin{center}
{\Large Answers}

{\Large \bigskip }
\end{center}

\begin{enumerate}
\item Solve each of the following system of linear equations by elimination.$%
\medskip $

a) \ $\left\{ 
\begin{array}{c}
3x+y=5 \\ 
2x-y=15%
\end{array}%
\right. $ \ \ \ \ \ \ c) \ $\left\{ 
\begin{array}{c}
3x+y=10 \\ 
5x-y=-2%
\end{array}%
\right. $ \ \ \ \ \ \ \ e) \ $\left\{ 
\begin{array}{c}
-2x+3y=-11 \\ 
5x-2y=0%
\end{array}%
\right. \medskip $

b) $\ \left\{ 
\begin{array}{c}
x+5y=32 \\ 
x-2y=-24%
\end{array}%
\right. $ \ \ \ \ \ \ d) $\ \left\{ 
\begin{array}{c}
4x+5y=12 \\ 
-3x+y=-9%
\end{array}%
\right. $ \ \ \ \ \ \ \ f) \ $\left\{ 
\begin{array}{c}
4x-5y=30 \\ 
7x+2y=-12%
\end{array}%
\right. \medskip \medskip $

a) \ $x=4,$ $y=-7$ \ \ \ \ \ \ \ \ b) \ $x=-8,y=8$ \ \ \ \ \ \ \ \ c) \ $%
x=1,y=7$ \ \ \ \ \ \ \ \ \ \ d) \ $x=3,y=0$ \ \ \ \ \ \ \ e) \ $x=-2,$ $y=-5$
\ \ \ \ \ \ \ \ f) \ $x=0$, \ $y=-6$

\item There is an animal farm where chickens and cows live. \ All together,
there are $53$ heads and $174$ legs. \ How many chickens and how many cows
are there on the farm? \ \ \ \ \  $19$ chickens and $34$ cows$\medskip $

\item The sum of two numbers is $73$, their difference is $29$. \ Find these
numbers. \ \ \ \  $22$ \ and $51\medskip $

\item We have some $\$10$ dollar bills and some $\$20$ dollar bills. \ How
many of each do we have if all together, we have $42$ bills and their total
value is $\$620$? \ \ \ \ \ \ \ $\ \ \ \ 22$ tens and $20$ twenties$\medskip 
$

\item We have some coins, all dimes and quarters. \ How many of each type of
coins do we have if all together, we have $83$ coins and their total value
is $\$15.50$? \ \ \ \ \ \ 

$35$ dimes and $48$ quarters
\end{enumerate}

\end{document}