Finding the currents in this circuit
Your KVL equations seem to be wrong. You should assign proper sign to voltage drop across an element in a loop. 
For example, in the first KVL equation, you are traversing the loop clockwise and the current \$I_1\$ is also assumed to be in the same direction, so the voltage change across R1 would be negative (i.e. \$-I_1R_1\$). The same thing applies to all KVL loops. Thus the equations become.

$$-I_1R_1-I_5R_5-I_4R_4=V_1$$
 $$I_6R_6+I_3R_3-I_4R_4=V_2$$
 $$-I_2R_2+I_5R_5+I_6R_6=V_2$$

Apart from this, you have also done a mistake while inputting equations properly to the wolfram equation solver. Here is the link which generated right result.