Question

The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9. What is the number? write a system of equation to slove the problem

Answer 1

Xy is the number

A) x + y = 7
B) 10y + x = 10x + y + 9
collecting terms of equation B
B) -9x + 9y = 9
multiplying A) by 9
A) 9x + 9y = 63  then adding it to equation B)
B) -9x + 9y = 9
18y = 72
y = 4
x = 3

The number is 34