A quite old, unanswered question which seems to have been moved just now from the PTC-Education-Forum to the Mathcad section here.
In case @MG_10870768 is still interested, here is a possible solution using the solve block:
The system seems to be very sensible with respect to the guess values. Using z:=1 it fails to find a solution, using z:=2 a different solution with a negative z-value is found. Trying to solve the system symbolically threw an "unknown error".