Confusion with regards to power lines and the power lost

[Coolamebe]

Ok, so the title was pretty vague, I'm not sure how to succinctly describe the confusion. Anyway, so I've learned that the power lost is P=I²R, and so by increasing the voltage, as P=VI and is constant, the current will be lowered, and thus the power lost will decrease.
I'm confused about a couple things. While my physics teacher was specifically talking about P=I²R, should not P=V²/R also give the value, and so by increasing the voltage we increase the power lost? Is this not a contradiction?
I feel like it could be remedied if the wires in power lines are not ohmic conductors and so half the math I did above is invalid.
Anyway, any help would be greatly appreciated, thank you!

 

[lychette]

The calculation relates to the power dissipated (lost) in the transmission cables so the voltage you need is the voltage across the cables. I think you are confusing this with the voltage across the load (at the end of the cables)

 

[Coolamebe]

The calculation relates to the power dissipated (lost) in the transmission cables so the voltage you need is the voltage across the cables. I think you are confusing this with the voltage across the load (at the end of the cables)

Can you explain this a little more in depth? My teacher explained this very superficially so I'm not too sure on this.