From the first equation, z=3y-4x. Substitute this in the other equations:
-2y-5(3y-4x)=6, -17y+20x=6 (1)
-4x+5y+2(3y-4x)=-2, 11y-12x=-2 (2)
(1)×3=-51y+60x=18, (2)×5=55y-60x=-10
Add these together to eliminate x: 4y=8, y=2, 22-12x=-2, 12x=24, x=2, z=3y-4x=-2.
SOLUTION (x,y,z)=(2,2-2)