Performing Mesh Analysis on h-parameter transistor models
You have a loading resistor That connects I2 to V2 by Ohms law. That's your missing equation. You can substitute I2 = -V2/RL. Now you have 2 equations still left which have variables V1, I1 and V2. Eliminate I1 and you get finally the wanted ratio of V2 and V1. 

(BTW: We others like to see V2/V1 named as the voltage gain, not V1/V2)

As well you can eliminate V2 and get V1/I1 which was the other wanted ratio.