Question 719734
X and Y are the digits.  The number is {{{10*X+Y}}}, taking care of place value for this two digit number.


First condtion:  {{{10X+Y=2(X+Y)}}}


Second condition, a bit complicated, but {{{10Y+X=-9+5(10X+Y)}}}.  


You should simplify each of those equations, and then solve for X and Y.  


First Condition: 10X+Y=2X+2Y,
..
{{{8X-Y=0}}}

Second Condition:  10Y+X-5(10X+Y)=-9
10Y+X-50X-5Y=-9
-49X+5Y=-9
{{{49X-5Y=9}}}


SYSTEM TO SOLVE:
{{{highlight(49X-5Y=9)}}}
{{{highlight(8X-Y=0)}}}


I tried solving both equations for y, equate them, and solve for the value of x...  {{{highlight(x-1)}}}.  Using that, 8*x-y=0, y=8*x, y=8*1, {{{highlight(y=8)}}}.
Number is 18.