You would be correct. Direct reasoning you already have your teacher who told you what would happen you are simply doing a reaction because of her.
Since x and y must be positive, 7x and 11y are positive either. That means 7x + 11y > 0. Then we would obtain N > 0 because 7x + 11y = N. That also means N must be positive. So if we set N to be zero or negative, there would be no solution. Thus, to produce an answer of No solution, the highest number N could be is 0.
A postulate isn't required to be proven
