Question 29957
The given problem is wrong because if you add both the equations not only do both the variables vanish but you get an afsurdity: 0 = -34 WHICH IS NOT MATH!
Let me give you one corrected version of the problem 
3x + y= 18  ----(1)
3x - y=  6  ----(2)
(1) + (2) implies
(3x+3x) = (18+6)
6x = 24
x = 24/6 = 4
x=4in (1) gives 
3X(4)+y = 18
12+y =18
y = 18-12 = 6
Answer: x =4 and y=6
Verification:Putting x =4 and y=6 in (2)
LHS = 3x-y = 12-6 =6 =RHS
Therefore our values are correct.