Question 103791
x+y = 28 (1)
x*y = 7  (2)
Note that it is not necessary to solve for x and y, since what is asked for is the sum of the reciprocals.  
Easiest way: Divide eqn (1) by eqn (2)
(x+y)/(x*y) = 4
Or x/(x*y) + y/(x*y) = 4 which reduces to 1/y + 1/x = 4