Question 921289
xy = 56
7(1/x) + 14(1/y) = 4


Simplify the second equation.
7/x + 14/y = 4
(7y + 14x)/(xy) = 4
7y + 14x = 4 * 56 = 224 ----> 2x + y = 32 ---> y = 32 - 2x


Substitute this into the first equation.


xy = 56
x(32 - 2x) = 56
-2x^2 + 32x - 56 = 0
x^2 - 16x + 28 = 0
(x - 2)(x - 14) = 0


x is the smaller integer, so x = 2 and y = 28.