I think you mean:
(1) x+y+z=-2
(2) 2x+5y+2z=-19
(3) -x+7y-3z=50
Using elimination:
(4)=(1)+(3)=8y-2z=48⇒4y-z=24
(5)=(2)-2(1)=3y=-15, y=-5
Substitute y=-5 in (4): -20-z=24, z=-44.
Substitute for y and z in (1): x-5-44=-2, x=47.
SOLUTION: x=47, y=-5, z=-44.