解方程三元一次方程 2x+3y+z=6 x-y+2z=-1 x+2y-z=5


2x+3y+z=伍模嫌6 (1)
x-y+2z=腔手-1 (2)
x+2y-z=5 (3)

(3)-(2)
3y-3z = 6
y-z = 2 (4)

2(3)-(1)
y-3z=4 (5)

(4)-(5)
2z=-2
z=-1

from (4)
y+1=2
y=1

from (3)
x+2 +1=码源5
x=2

(x,y,z)=(2,1,-1)
x=2 y=1 z=-1
2x+3y+z=6(1)
x-y+2z=-1(2)
x+2y-z=5(3)
消纤启x,(2)x2 2x-2y+4z=-2(4)
(1)-(4) 5y-3z=8(5)
(3)-(2) 3y-3z=6 y-z=2(6)
y=2+z(7)
把(毁型如7)代入(5) 5(租山2+z)-3z=8
10+5z-3z=8
2z=-2
z=-1
y=2-1=1
x=5-2y+z=5-2-1=3-1=2
x=2
y=1
z=-1