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{Mathematical Physics --- PHZ 3113}\\\vspace {2mm} 
Classwork 13 (April 10, 2013) \\ Linear Equations
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After finding solutions: Check that they are correct!

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\noindent 1. Find all solutions of the equations
\begin{eqnarray} \label{Eq1a}
   x + 2y &=& 3\,,\\ \label{Eq1b} 3x +  y &=& 2\,.
\end{eqnarray}
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\noindent 2. Find all solutions of the equations
\begin{eqnarray} \label{Eq2a}
   x + 2y &=& 3\,,\\ \label{Eq2b} 2x + 4y &=& 6\,.
\end{eqnarray}
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\noindent 3. Find all solutions of the equations
\begin{eqnarray} \label{Eq3a}
   x + 2y &=& 3\,,\\ \label{Eq3b} 2x + 4y &=& 4\,.
\end{eqnarray}
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\noindent 4. Find all solutions of the equations
\begin{eqnarray} 
   x + 2y &=& 0\,,\\ 3x +  y &=& 0\,.
\end{eqnarray}
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\noindent 5. Find all solutions of the equations
\begin{eqnarray} \label{Eq5a}
   x + 2y &=& 0\,,\\ \label{Eq5b} 2x + 4y &=& 0\,.
\end{eqnarray}
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\noindent 6. Find all solutions of the equations
\begin{eqnarray} \label{Eq6a}
   x + 2y +  z &=& 0\,,\\ \label{Eq6b} 
  2x + 4y +  z &=& 0\,,\\ \label{Eq6c}
   x +  y + 2z &=& 0\,.
\end{eqnarray}
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\noindent 7. Find all solutions of the equations
\begin{eqnarray} \label{Eq7a}
   x + 2y +  z &=& 0\,,\\ \label{Eq7b} 
  2x + 4y + 2z &=& 0\,,\\ \label{Eq7c}
   x +  y + 2z &=& 0\,.
\end{eqnarray}
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