b

17x + 5 = n
23y + 14 = n

17x + 5 = 23y + 14
17x - 23y = 14 - 5 = 9

When the integer n is divided by 17, the quotient is x and the remainder is 5.
i.e. n = (17*x) + 5 -(Equation 1)

When n is divided by 23, the quotient is y and the remainder is 14.
i.e. n = (23*y) + 14 -(Equation 2)

Which of the following is true?
Equating Equation 1 and Equation 2, we get n = (17*x) + 5 = (23*y) + 14
(17*x) - (23*y) = 9
Answer B

Note that if 5 was subtracted from n and then divided by 17, the quotient would be exactly x with a 0 remainder:

(n- 5)/17 = x

Similarly:

(n - 14)/23 = y

Forming a relationship between the two:

n - 14 = 23y => n - 5 = 23y + 9

23y + 9 = 17x

23y - 17x = -9 => 17x - 23y = 9

Choose B.