Can someone tell me if I did this right because my solution seems wrong, but I've done it a couple times and get the same answer. I'm given the following:
x' + 2y' + x = 0
x' - y' + y = 1
and the initial values of x(0) = 0 and y(0) = 1
The idea is to solve this initial value problem.

Can someone please tell me if this is right? Thanks.

That's not at all the way I would do the problem (I detest "Laplace transform") but that's exactly what I got as the answer: x(t)= 0 and y(1)= 1. Of course, you could have checked that yourself. Since x and y are constants, there derivatives are 0 and the equations reduce to 0+ 2(0)+ 0= 0 and 0- 0+ 1= 1.