SOLUTION: The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9. What is the number? I know that the answer is 34, and I know that one

Question 130267: The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9. What is the number?
I know that the answer is 34, and I know that one of the equations is x+y=7, but I do not know the other part to the system of equations. Thanks for helping me!!!
Answer by ilana(307) (Show Source): You can put this solution on YOUR website!
If you want one of the equations to be x+y=7, that means the digit is xy. So if the number is 25, x=2 and y=5. to get 25 from 2 and 5, you need to think about place value. There are 2 tens and 5 ones, so 25=2(10)+5(1). (Notice, this is true.) So in general, for a number xy, the number is 10x+y. If we reverse the digits in the number, we get yx=10y+x. So the second equation is
(10y+x)-(10x+y)=9. This simplifies to 10y+x-10x-y=9, or 9y-9x=9, or y-x=1. So our two equations are x+y=7 and y-x=1. Solve the second for y and get y=x+1. Plug that y into the first and get x+(x+1)=7, so 2x+1=7, 2x=6, x=3. If x=3, y=(3)+1=4. So the number is 34. Check that that number fulfills both conditions.
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