Let P (x, y) be a moving point on the ellipse x216 + Y29 = 1, then the maximum value of X + y is______ ．

∵ P (x, y) is a moving point on the ellipse x216 + Y29 = 1. Let x = 4cos θ, y = 3sin θ, ∵ x + y = 4cos θ + 5sin θ = 5sin (θ + ∞), and the maximum value of ∵ is 5, so the answer is: 5

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