Question

2x+y-z=5 x-y+2z=-1 x+2y+z=-2

Answer 1

2x+y-z=5 ................(1)
x-y+2z=-1................(2)
x+2y+z=-2................(3)

(1)*2+(2)得
5x+y=9................(4)
(1)+(3)得
3x+3y=3
x+y=1................(5)

(4)-(5)得
4x=8
x=2
代入(5)得
2+y=1
y=-1
代入(1)得
4-1-z=5
z=-2

解得
x=2
y=-1
z=-2

Answer 2

2x+y-z=5 (1)
x-y+2z=-1 (2)
x+2y+z=-2 (3)
(1)×2+(2)
5x+y=9 (4)
(1)+(3)
3x+3y=3
x+y=1 (5)
(4)-(5)
4x=8
所以x=2
y=1-x=-1
z=2x+y-5=-2