The question asks to determine V_x and I_y.
I tried to find it by using KVL in to lower LHS mesh and KCL in the middle node. But, my final value is a contradictory statement(such as I_x equal all real numbers). Any help would be appreciated.
Using KCL in the central node, the current that passes through the 10 ohm resistor is -5-0.1V_x+y(where y is the current that goes through V_x/20 ohms resistor). Then I used KVL in lower LHS mesh, so -50-10(-5-0.1V_x+y)-V_x=0 As you can see V_x cancel and 10y=0 is left. However V_x=20y.