If positive integers x and y satisfy the equation xy−5x−10y+43=0, the sum x+y is constant. What is the value of x+y?

Answer 1

factor it and re-arrange

y(x-10) = 5x - 43
y = (5x-43)/(x-10)

for y to be positive, 5x > 43 and x >10

if x = 11 , y = 12/1 = 12

so x+y = 11+12 = 23