3a + b + c = -3 (1)
a + 3b + c = 9 (2)
a + b + 3c = -6 (3) add all three equations
4a + 4b + 4c = 0
a + b +c = 0
a + b = -c sub this into (3)
-c + 3c = -6
2c = -6
c = - 3
Also a + c = -b sub this into (2)
-b + 3b = 9
2b = 9
b = 9/2
And a + b + c =0
a + 9/2 - 3 = 0
a + 3/2 =0
a = -3/2
abc = (-3/2)(9/2) (-3) = 81 / 4