A problem of ideal transformer
Many of us have quite low brain capacity. For example your equations have too much variables at least for me. I can't at a glance see, is somewhere an error. But here's one proper solution. The facts are collected to equations with smaller number of variables:


The equations are


Kirchoff's current laws in nodes A and B 
an expression for the current of R2 (actually it's Kirchoff's voltage law in loop R2-R3-transformer) 


All terms are moved to the left side to get zeros to the right sides.

The solution is found by MS Excel Solver:



The orange area has the modified variables. The blue area has the left sides of the three equations. The yellow area is the goal - make this zero. It's the sum of the squares of the left sides.

The result: V0 = 48V