Applying Cramer's rule to find out the transfer function of the circuit
I don't know about Cramer's rule but I'd solve it like this.


The dot notation on the coupled inductors is of no consequence except to put a minus sign in front of the final TF. Don't forget to do that!
The coupled inductors can be made into three joined inductors: -




The fact that there is no galvanic isolation is of no consequence to calculating the TF.

Now, the circuit boils down to this: -







simulate this circuit &ndash; Schematic created using CircuitLab

Can you take it from here?