Why supernode approch results wrong answer?
Perhaps I have missed something, you are not 100% consistent in your naming of things. IE in the hand written drawing you have the center node labeled "1" but in the schematic it is labeled "2".

Anyways, the answer I get agrees with the given answers. I solved it using 4 current loops. Your mistake is when you multiply equation (i) by 3, you do not multiply 1620 by 3.

You have
(i)
$$
V_1 -5V_3 +10V_4 -1620 = 0
$$

You then attempt to multiply by 3 to eliminate \$ V_3 \$.

You have

$$
3V_1 -15V_3 +30V_4 = 1620
$$

But it should be

$$
3V_1 -15V_3 +30V_4 = 4860
$$

HTH