3X+Y+2Z=11 ①
2X+Y+3Z=12 ②
X-Y-4Z=-9 ③
①-②,得X-Z=-1 ④
②+③,得3X-Z=3 ⑤
⑤-④,得2X=4,解得X=2
代入④,解得Z=3
代入③,得2-Y-12=-9,解得Y=-1