Given equations can be rewritten as
x(x+y+z)=18
y(x+y+z)=−12
z(x+y+z)=30
Adding (1),(2) and (3), we get
(x+y+z)2=36 or x+y+z=±6
Then from (1) and (4), we get x=±3
Similarly from (2) and (4),y=∓2,
and from (3) and (4), z=±5.
Hence the solutions are
x=3, y=−2, z=5
or x=−3, y=2, z=−5.