Supernode for nodal analysis with independent voltage sources

[@aerodynamico6427]

At 7:02, When you add V4 and G14 to the circuit, the additional new path from V1 has a current of (V1 - V4)xG1, not -V4xG1.

[@abhirammsd357]

Can you illustrate any example problem for this?
For even more clarity with this concept.