Find the solution to the given system of IVPs.
\[ 4 \, {x} + {x'} = 2 \, {y} \hspace{2em}x(0)= 1 \]
\[ 0 = -{y'} - 2 \, {x} - 9 \, {y} \hspace{2em}x(0)= 1 \]
Answer:
\[x= 2 \, e^{\left(-5 \, t\right)} - e^{\left(-8 \, t\right)} \]
\[y= -e^{\left(-5 \, t\right)} + 2 \, e^{\left(-8 \, t\right)} \]