X+Y+Z=2 (1)
3X-Y-4Z=5 (2)
2X+3Y-2Z=0 (3)
(1)+(2)
4X-3Z=7 (4)
(2)×3+(3)
11X-14Z=15 (5)
(4)×14-(5)×3
56X-33X=98-45
23X=53
X=53/23
Z=(4X-7)/3=17/23
Y=2-X-Z=-24/23