The product of two positive integers is equal to twice their sum. This product is also equal to six times the difference between the two integers. What is the sum of these two integers?

a b = 2 (a + b)...............(1) a b = 6 (a - b)................(2)

2[a +b] =6[a - b] 2a +2b =6a - 6b a = 2b Sub into equation (1) 2b^2 - 6b = 2b(b - 3) = 0 b(b - 3) =0 b = 3 and a=6

x+y=9