Solving system of coupled PDE

Hi,

I was trying to solve the following system of PDE:

dx/dz = - (x-y)

dy/dt = (x-y)

with the following initial contion: t=0, y=0

and limit condition: z=0, x=1

I tried to use pdepe with any success, maybe someone could point me to the right direction.

I was reading the other post but not sure if I have to use anothe method to solve this.

Thanks