show that the IVP $x' = Ax + f(t),\,\,\ x(0) = x_0$ is transformed into a linear system of equations by the Laplace transform.

Question

show that the initial value problem

$x' = Ax + f(t),\,\,\ x(0) = x_0$

is transformed into a linear system of equations by the Laplace transform.

I have tried to apply the Laplace transform in both members of the equation and then use that $\mathcal{L} (x') (s) = s\mathcal{L} (x) (s) - x (0)$, but I can not find a linear system from there. Does anyone have any ideas ?