Question 557603
Let x = the 10's digit
Let y = the units
then
10x+y = the two-digit number
:
A two-digit number is eight times the sum of its digit.
10x + y = 8(x + y)
10x + y = 8x + 8y
10x - 8x + y - 8y = 0
2x - 7y = 0
:
 When the number is added to the number obtained by reversing the digits, the sum is 99. Find the original number.
10x+y + 10y+x = 99
11x + 11y = 99
simplify, divide by 11
x + y = 9
Multiply this equation by 2, subtract the 1st equation
2x + 2y = 18
2x - 7y = 0
-------------subtraction eliminates x, find y
9y = 18
y = 2
then
x + 2 = 9
x = 7
:
72 is the number, you can check this in both statement equations: