0001.tex

\begin{exerciseStatement}


Find the solution to the given system of IVPs.

\[ 0 = -4 \, {x} - 4 \, {y} - {x'} \hspace{2em}x(0)= -5 \]\[ 9 \, {x} + {y'} = {y} \hspace{2em}x(0)= 8 \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[x= -4 \, e^{\left(5 \, t\right)} - e^{\left(-8 \, t\right)} \]\[y= 9 \, e^{\left(5 \, t\right)} - e^{\left(-8 \, t\right)} \]
\end{exerciseAnswer}