Find $y(t)$ and $z(t)$ when $x(t)=u(t),$ where $u(t)$ is a step function, by solving the following system of ordinary differential equations using the Laplace Transform:

$\frac{dy}{dt}+2y+z=\frac{dx}{dt}+x$

$\frac{dz}{dt}+3z+2y=x$

for zero initial conditions.