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\begin{document}

\begin{enumerate}

\item  Solve
\[
\begin{array}{rrrrrr}
x & = & y & + & 3 \\
x & = & y^2 & + & 1 \\
\end{array}
\]

\item  Solve
\[
\begin{array}{rrrrrrr}
x & + & y & + & z & = & 2 \\
-x & + & 3y & + & 2z & = & 8 \\
4x & + & y &  &  & = & 4 \\
\end{array}
\]

\item  Solve
\[
\begin{array}{rrrrrrr}
x & - & 3y & + & 2z & = & 18 \\
5x & - & 13y & + & 12z & = & 80 \\
\end{array}
\]

\item  Find the equation of a quadratic function $f(x)=ax^2+bx+c$ that passes through the points: $(-1,3), (1,1), (2,6)$

\item  Find the partial fraction decomposition for:
\[
\frac{6}{x^2-9}
\]

\item  Find the partial fraction decomposition for:
\[
\frac{x^2-1}{x(x^2+1)}
\]

\item  Find the partial fraction decomposition for:
\[
\frac{3x+1}{(x-1)^2}
\]

\item  Graph the system of inequalities.  Label the points of intersections(the vertices).
\[
\begin{array}{rrrrr}
x & + & y & \leq & 1 \\
-x & + & y & < & 1 \\
  &  & y & > & 0 \\
\end{array}
\]

\item  Graph the system of inequalities.  Label the points of intersections(the vertices).
\[
\begin{array}{rrrrr}
3x & + & 2y & < & 6 \\
x & + & 4y & > & -2 \\
2x  & + & y & \leq & 3 \\
\end{array}
\]

\item  Find the maximum and minimum of $z=2x-5y$ subject to the constraints :
\[
\begin{array}{ccccc}
& & x & \geq & 0 \\
& & y & \geq & 0 \\
2x & + & y & \leq & 6 \\
\end{array}
\]

\end{enumerate}
\end{document}

