To Find the Transfer Function Z(s)/X(s) for the system....

Question

Please, help me to answer the next problem:

Objective: To find the Transfer Function $z(s)/x(s)$ for the system, using the next equations:

"$a$", "$b$", "$c$" y "$k$" are constants

1. $x(t) = a y(t) + b y'(t)$
2. $w(t) = k y(t)$
3. $w(t) = c z(t) + g z'(t)$

Answer 1

Hint: If we take the Laplace Transform of each equation, we get:

1. $X(s) = aY(s)+bsY(s) = (a+bs)Y(s)$
2. $W(s) = kY(s)$
3. $W(s) = cZ(s)+gsZ(s) = (c+gs)Z(s)$

Can you combine these equations to get $\dfrac{Z(s)}{X(s)}$?