2X-Y+Z=-3 (1)
X+3Y-2Z=13 (2)
3X-2Y-Z=2 (3)
(1)*2+(2): 5X+Y=7 (4)
(1)+(3): 5X-3Y=-1 (5)
(4)-(5): 4Y=8
Y=2
5X+2=7
5X=5
X=1
3-4-Z=2
Z=-3
X=1, Y=2, Z=-3
2X-Y+Z=-3 (1)
X+3Y-2Z=13 (2)
3X-2Y-Z=2 (3)
(1)*2+(2): 5X+Y=7 (4)
(1)+(3): 5X-3Y=-1 (5)
(4)-(5): 4Y=8
Y=2
5X+2=7
5X=5
X=1
3-4-Z=2
Z=-3
X=1, Y=2, Z=-3