\documenttype{article}
\title{Math 587 Assignment 2}
\author{John Doe}
\date{March 3, 2009}
\begin{document}



\begin{enumerate}
\item  At what point does the line $2 x - y = 3$ intersect the
line $x + 2y = -1$?

\emph{Solution.}  
The point of intersection may be obtained by solving the two
equations simultaneously.  For this multiply the first equation
by $2$ and add that to the second equation obtaining the equation
\[ 5 x = 5 \ . \]
Thus, $x = 1$, and, using either of the two original equations,
one finds $y = -1$.  The required point is $(1, -1)$.

\item  Find all solutions of the quadratic equation
$x^2 - x - 12 = 0$.

\emph{Solution.} The well known formula for solution of
the quadratic equation $ax^2 + b x + c = 0$ is
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \ . \]
In this case one finds
\[ x = \frac{1 \pm \sqrt{1 -4(1)(-12)}}{2}
     = \frac{1 \pm 7}{2}
     = 4 \ \mbox{or} \ -3 \ .\]

\end{enumerate}

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