Sorry, my first answer was completely wrong^^.
2x-y+z=-5 ---------(1)
5x+2y-2z=19 ------(2)
x-3y+z=-5-----------(3)
2*(1)+(2): 4x-2y+2z=-10
+ 5x+2y-2z=19
-------------------------
9x=9 ---> x=1
(2)+2*(3) 5x+2y-2z=19
+ 2x-6y+2z=-10
---------------------------
7x-4y=9 --->since x=1, 7*1-4y=9 --> 7-9=4y --> y=-1/2
(3) x-3y+z=-5 --> since x=1, y= -1/2, --> 1-3(-1/2)+z=-5 --> 1+3/2+z=-5 --> z=-5-5/2 = -15/2
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