Cancelling Out with Hess's Method

[Sophia Diaz - Dis 1B]

In class we did an example with NO2 formation:

N2 + O2 --> 2NO
2NO + O2 --> 2NO2
----------------------
N2 + 2O2 --> 2NO2

The way we got the third and final reaction was by adding the first two and the 2NO's "canceled out."
I don't really understand how the 2NO's canceled out but the O2's did not. Why did only the 2NO's get canceled out in order to get the final equation?

[Theodore_Herring_1A]

The 2NOs cancel out because one is a reactant and the other is a product. The O2s do not cancel out since they are both reactants, and thus they are added together.

[Ethan Yi 1K]

the 2NO's are on opposite sides of the equation and therefore will cancel out. however, the O2's are on the same side, so you add them together.

[Jocelyne Milke 1G]

You can only cancel things out when you have the same compound on the reactants side and the products side.