Question 130267
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.