1. The problem statement, all variables and given/known data I've attached the problem. 2. Relevant equations L(1) = 1 /s L(t^n) = n!/s^(n+1) 3. The attempt at a solution because the question only asks for X(s) I only considered the x' + x + 4y=3 equation. I applied laplace tranforms and got: s X(s) - x(0) + 1/s^2 + 4/s^2 = 3/s. since x(0) = 0 it gets cancelled out so.. s X(s) + 5/s^2 = 3/s s X(s) = 3/s - 5/s^2 therfore X(s) = (3/s - 5/s^2) / s only problem is, i didn't use the other equation which makes me feel i've done it wrong.