SOLUTION: find a two digit number such that three times the tens digit is 2 less than twice the unit digit, and twice the number is 20 greater than the number obtained by reversing the digit

Question 1020657: find a two digit number such that three times the tens digit is 2 less than twice the unit digit, and twice the number is 20 greater than the number obtained by reversing the digit?
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Let's call the number xy, where x is the tens digit and y, the ones digit. This number has a VALUE of 10x+y. Then we write
3x = 2y - 2 and
2(10x+y) = 20 + (10y+x)
Now we work out for x and y...
20x + 2y = 20 + 10y + x
-------------------
We have to solve the system
19x - 8y = 20
3x - 2y = -2
----------------------
Multiply the bottom one by 4 and subtract...we get
19x - 8y = 20
-(12x - 8y = -8)
----------------
7x = 28
x = 4
And if x = 4, then
3(4) - 2y = -2
12 - 2y = -2
-2y = -14
y = 7
The number is 47.
How's that?

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