Question 464737
Let xy be the unknown number. ==> x = tens digit, and y = ones digit.

Then from the given, 8(x+y) + 1= 10x + y, and 13(x-y) + 2 = 10x + y.

<==> 2x - 7y = 1 and -3x + 14y = 2

Proceeding with the method of elimination, we get x = 4 and y = 1.  (Check these solution against the original system!)

Therefore the number is 41.