When you reverse the digits in a certain two-digit number you decrease its value by 9. what is the number if the sum of its digits is 7?

Let xy be this number, where x is the tens and y, the units.(xy is not the product of x times y, it's just a number with 2 digits))
(Mind you xy can be written as 10x+y, just like 25 - 2.10 + 5)

Now let's translate English into Math:

1) x+y =7 (note that the reverse of xy is yx or 10y+x)

2) 10y+x = (10x+y) -9 →-9x +9y = -9

1)    x+y =7
2) - 9x +11y = -9

Solving these equations will give:

x = x=4 and y = 3. Hence the number is 43