SOLUTION: The sum of the digits of a two-digit number is 14. When the digits are reversed, the resulting number is 23 less than two times the original number. What is the original number?
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Question 417381: The sum of the digits of a two-digit number is 14. When the digits are reversed, the resulting number is 23 less than two times the original number. What is the original number? Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! x-- ten's digit
y --- unit's digit
x+y =14........1
10y+x= 2(10x+y)-23
10y+x=20x+2y-23
8y-19x=-23............2
x+y=14 .............1
-19x+8y= -23.............2
multiply (1)by -8
Multiply (2) by 1
-8x-8y=-112
-19x+8y= -23
Add the two equations
-27x=-135
/-27
x=5
plug value of x in (1)
x+y=14
5+y=14
y=14-5
y=9
Number is 59
y = 9
