Explanation

9ˣ3ʸ = 3^{2x+y} = 2187 = 3⁷ gives 2x + y = 7. The second equation gives 2^{3x+2y} = 2^{2xy}, so 3x + 2y = 2xy. With y = 7 − 2x: 3x + 14 − 4x = 14x − 4x², i.e. (4x−7)(x−2) = 0. The listed possibility is x = 2, y = 3, so x + y = 5: option C.