Question 845681
First recheck how you did your elimination process.  Notice both equations use "2y".  Subtract one equation from the other to eliminate terms of y:


{{{(3x+2y)-(2x+2y)=5-38}}}
{{{x=-33}}}, as you seem to have found.
Not trying to eliminate x, 2y=5-3x, {{{y=5/2-3x/2=(5-3x)/2}}},
Substituting for x: {{{y=(5-3(-33))/2=(5+99)/2=104/2=52}}}, again just as you found.  


Probably no theoretical meaning for the sum of the solutions of x and y, at least none that seem apparent.  Just compute "the sum of the solutions".


{{{highlight(-33+52=19)}}}


Interesting how the first equation's sum of coefficients give the constant term on the right member, as 3+2=5.  It was just (a guess) setup like that.  Also see that the second equation is equivalent to x+y=19... but this is exactly what the question asked!  The sum of the solution of x and y was found to be 19.