SOLUTION: A two digit number is obtained by either multiplying the sum of the digits by 8 and adding 1, or by multiplying the difference of the digits by 13 and adding 2. Find the number

Question 464737: A two digit number is obtained by either multiplying the sum of the digits by 8 and adding 1, or by multiplying the difference of the digits by 13 and adding 2. Find the number
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
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.
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