解三元一次方程组1、x+y-z=4 2x-y+z=5 x-3y+z=-2 2、y+2z=-2 3x+y-4z=1 2x-y+2z=8 3、x-2y+z=-1 x+y+z=2

题目

解三元一次方程组1、x+y-z=4 2x-y+z=5 x-3y+z=-2 2、y+2z=-2 3x+y-4z=1 2x-y+2z=8 3、x-2y+z=-1 x+y+z=2
x+2y+3z=-1

答案

1.x+y-z=4 2x-y+z=5 x-3y+z=-2 (x+y-z)+(2x-y+z)=4+5 3x=9 x=3
(2x-y+z)-(x-3y+z)=5-(-2) x+2y=7 把x=3代入x+2y=7可得 3+2y=7 2y=4 y=2
把x=3,y=2代入x+y-z=4 可得 3+2-z=4 5-z=4 z=1
2.y+2z=-2 3x+y-4z=1 2x-y+2z=8 (y+2z=-2)×2可得2y+4z=-4 (3x+y-4z)+(2y+4z)=1-4
3x+3y=-3 x+y=-1 (x+y=-1)×2可得2x+2y=-2 (2x-y+2z)-(y+2z)+(2x+2y)=8-(-2)-2
4x=8 x=2 (2x-y+2z)-(y+2z)=8-(-2) 2x-2y=10 x-y=5 把x=2代入x-y=5 可得 2-y=5 y=-3
把y=-3代入y+2z=-2可得 -3+2z=-2 z=0.5
3、x-2y+z=-1 x+y+z=2 x+2y+3z=-1 (x-2y+z)-(x+y+z)=-1-2 -3y=-3 y=1 把y=1代入x-2y+z=-1 可得 x-2+z=-1 x+z=1 (x+2y+3z)-(x+z)=-1-1 2y-2z=-2 y-z=-1 把y=1代入y-z=-1 可得 1-z=-1 z=2 把y=1,z=2 代入x+y+z=2 可得 x+1+2=2 x=-1