0006.tex

\begin{exerciseStatement}


Find the solution to the given system of IVPs.

\[ 0 = 2 \, {y} + {x'} - 4 \, {x} \hspace{2em}x(0)= -3 \]\[ 0 = -7 \, {y} + 2 \, {x} + {y'} \hspace{2em}x(0)= 1 \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[x= -e^{\left(8 \, t\right)} - 2 \, e^{\left(3 \, t\right)} \]\[y= 2 \, e^{\left(8 \, t\right)} - e^{\left(3 \, t\right)} \]
\end{exerciseAnswer}