Question 708709
Two-digit number, {{{10*T+U}}}
{{{9+10T+U=10U+T}}}
.
{{{9T=-9+pU}}}
{{{9T=9U-9}}}
{{{T=U-1}}}


A graph of this linear equation helps to see how the digits would work.  Tens as a function of the Units.

{{{graph(300,300,0,10,0,10,x-1)}}}


The vertical axis intercept is not important.  We only deal with digits which themselves are positive numbers.  The tens cannot here be zero since we require a TWO digit number.  Our tens must be at least a 1, and so by the line present (or our equation), 12 is our smallest possible number, and 89 is our largest possible number.  Reminder:  TWO-digit number.  For any allowable Unit digit or Ten's digit, we can read the corresponding Ten's digit or Units digit.  


We can check that 12 works.  12+9=21.
We can check that 89 works.  89+9=98.

We can check any other arrangement:  56+9=65.