2x + 2y + z = -5 ⇒ -4x - 4y - 2z = 10 (1)
3x + 4y + 2z = 0 (2)
x + 3y + 2z = 1 (3)
Add (1) and (2) giving
-x = 10 ⇒ x = -10
Add (1) and (3) giving
-3x - y = 11 sub for x
-3(-10) - y = 11
30 - y = 11
y = 19
So using (3) to find z, we have
-10 + 3(19) + 2z = 1
-10 + 57 + 2z = 1
47 + 2z = 1
2z = -46
z = -23
So......{x,y,z} = {-10, 19, -23}