0006.tex

\begin{exerciseStatement}


Find the solution to the given system of IVPs.

\[ -{x'} - 4 \, {y} = -5 \, {x} \hspace{2em}x(0)= -3 \]\[ {y'} + {x} = 8 \, {y} \hspace{2em}x(0)= -2 \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[x= e^{\left(9 \, t\right)} - 4 \, e^{\left(4 \, t\right)} \]\[y= -e^{\left(9 \, t\right)} - e^{\left(4 \, t\right)} \]
\end{exerciseAnswer}