Calculate currents in thevenin equivalent methods
You begin with an incorrect statement:
$$10(I_1-I_2)=0$$

You're saying that the voltage across the current controlled current source is 0 which is very likely incorrect. You can say $$10(I_1-I_2) = V_\text{node_between_CCCS_and_12Vsource}$$

But you can't assume that that voltage equals 0. If you have some current flowing through that resistor, then the voltage can not be 0.

Other than that, your equations look good. These should be them:

$$ 4.5\times I_a = I_1 $$ 

$$ 10(I_1-I_2)+12+40*(I_3-I_2)=0  $$
$$ 40\times(I_3-I_2)-5I_3=0  $$
$$ I_a = I_2-I_3  $$ 

4 equations and 4 unknowns. You should be golden to solve it from here.