Solve the following initial value problems using Laplace transforms:
dx(t)/dt - 6y(t) = -125e⁻³ᵗ
dy(t)/dt - x(t) + y(t) = 0
Given initial conditions: x(0) = 5, y(0) = 10
By applying Laplace transforms, compute X(s) = L(x(t)), Y(s) = L(y(t)).