Question 151788
Your initial equations look good!
3x+2y = 44
y = 2x-8 Substitute this  into the first equation.
3x+2(2x-8) = 44 Simplify.
3x+4x-16 = 44
7x-16 = 44
7x = 60
x = 60/7
y = 2x-8
y = 2(60/7)-8
y = 120/7 - 56/7
y = 64/7
Well, mathematically, these are the solutions. 
Was there anything in the instructions that led you to believe that the answers should be integers, besides the fact that you would normally expect integer answers in problems like this?