SOLUTION: The difference of the digits of a 2-digit number is 5. If the digits are reversed, the new number is 7 greater than twice the original number. What is the units digit of the origin

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Question 426896: The difference of the digits of a 2-digit number is 5. If the digits are reversed, the new number is 7 greater than twice the original number. What is the units digit of the original number?
Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
y-x =5
10y+x= 2(10x+y)+7
10y+x=20x+2y+7
8y-19x=7
-x+y=5 .............1
-19x+8y=7.............2

multiply (1)by -8
Multiply (2) by 1
8x-8y=-40
-19x+8y=7

Add the two equations

-11x = -33

/-11

x= 3

plug value of x in (1)

-x+y=5
-3+y=5
y=5+3
y=8
The number is 38