in a positive number of two digits,the sum of the digits is 15,if the digits are interchanged, the number is increase by 9.find the number

x y = y + 10 x

y x = 10 y + x
x+y = 15
10 x + y + 9 = 10 y + x
9 x - 9 y = -9
so
x + y = 15
x - y = -1
---------------- add
2 x = 14
x = 7
then y = 8
number = x y = 78
==================
check
87 -78 = 9 sure enough