Call the equations A, B and C.
B-A=2y+2z=6, y+z=3, so we can substitute z=3-y in A, B, C:
3x+5y+12-4y=25, 3x+7y+18-6y=31, 11x-2y+24-8y=17;
3x+y=13, 3x+y=13, 11x-10y=-7. Substitute y=13-3x into 11x-10y=-7:
11x-130+30x=-7, 41x=123, x=3; y=13-9=4; z=3-4=-1
SOLUTION: x=3, y=4, z=-1.