\begin{exerciseStatement}
Draw a phase plane for the following system of ODEs.
\[x'= 3 \, x - 2 \, y - 15 \]\[y'= 5 \, x + 3 \, y - 6 \]
Be sure to include and label the following features in your sketch:
\begin{itemize}
\item The isoclines \(x'=0\) and \(y'=0\).
\item Arrow systems describing trajectories of solutions.
\item The equillibrium of the system.
\end{itemize}
\end{exerciseStatement}
\begin{exerciseAnswer}
The isoclines cross at the equillibrium \( \left(3, -3\right) \), with \(x'=0\) having a positive slope and \(y'=0\) having a negative slope.
The right region has a northeast arrow system, the top region has a northwest arrow system, the left region has a southwest arrow system, and the bottom region has a southeast arrow system.
\end{exerciseAnswer}
