The sum of the digits of a certain two-digit number is 9. When you reverse its digits you increase the number by 45. What is the number?

Question

My teacher said that we should use a equation. For all of my other homework questions, they were using the elimination method. I don't know how to use those numbers by writing 2 equations.

Answer 1

Let x = ten's digit and y = one's digit

x+y = 9

10x+y = 10y+x+45

x + y = 9

9x - 9y = 45

Multiply the first equation by 9:

9x + 9y = 81

9x - 9y = 45

Add the equations to get 18x = 126

x = 7 and y = 2

The number is 72.