0009.tex

\begin{exerciseStatement}


Find the solution to the given system of IVPs.

\[ -{y} + 4 \, {x} = {x'} \hspace{2em}x(0)= -2 \]\[ -7 \, {y} = -{y'} - 4 \, {x} \hspace{2em}x(0)= 3 \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[x= -e^{\left(8 \, t\right)} - e^{\left(3 \, t\right)} \]\[y= 4 \, e^{\left(8 \, t\right)} - e^{\left(3 \, t\right)} \]
\end{exerciseAnswer}