You don't need Laplace Transforms...
Take the second derivative of the first DE to get
, which means
This is a second order linear non homogeneous constant coefficient ODE. You should know how to solve this.
The following question i am having trouble solving
Use Laplace Transforms to solve each system of differential equations
given x(0) = -1, y(0) = 1
This is what i have done:
I used cramers rule to find X and Y