0001.tex

\begin{exerciseStatement}


Find the solution to the given system of IVPs.

\[ -{y} = {x'} + {x} \hspace{2em}x(0)= 0 \]\[ 0 = 4 \, {x} - 6 \, {y} - {y'} \hspace{2em}x(0)= -3 \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[x= e^{\left(-2 \, t\right)} - e^{\left(-5 \, t\right)} \]\[y= e^{\left(-2 \, t\right)} - 4 \, e^{\left(-5 \, t\right)} \]
\end{exerciseAnswer}