To check, all you have to do is to see if your solution satisfies both equations.
Your solution satisfies the first, but not the second, so there is an erro
from the first: y = 12-x
first I would multiply the second by 2 to get rid of fractions
2x + 3y = 3
now sub in the first
2x + 3(12-x) = 3
2x + 36 - 3x = 3
-x = -33
x = 33
then y = 12-33 = -21
x = 33 , y = -21
LS = x+y = 33-21 = 12 = RS
LS = x + (3/2)y = 33 + (3/2)(-21)
= 33 - 31.5 = 1.5 = 3/2 = RS
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