First equation can be reduced:
(1) 2x-y+2z=18;
(2) 4x-3y-2z=-12;
(3) x-y+4z=27;
(1)+(2): (4) 6x-4y=6⇒3x-2y=3;
2(2)+(3): (5) 9x-7y=3;
3(4)-(5): (6) y=6⇒3x=3+12=15⇒x=5⇒10-6+2z=18⇒z=7.
SOLUTION: x=5, y=6, z=7.
CHECK
10-6+14=18✔️; 20-18-14=-12✔️; 5-6+28=27✔️.