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3x + 6y = 47

6y = -3x + 47

y = -3x/6 + 47/6

y = (-3x + 47)/6

Since we are looking for positive integer, 3x (x > 0) cannot be greater than 47, the possibilities of the numerator are 42, 36, 24, 18, 12, and 6, so that - 3x must be -5, -11, -23, -29, -35, and -41. Since any of them are not multiples of -3, we can not find any pair of positive integers that satisfy the equation. So x and y cannot be both positive integers.

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