Find $x(t)$ and $y(t)$ which satisfy

$$\begin{aligned} &3 \dot{x}+\dot{y}+5 x-y=2 e^{-t}+4 e^{-3 t} \\ &\dot{x}+4 \dot{y}-2 x+7 y=-3 e^{-t}+5 e^{-3 t} \end{aligned}$$

subject to $x=y=0$ at $t=0$.