解三元一次方程组:x-y+z=0,2x+y-2z=6

{x-y+z=0,①
2x+y-2z=6,②
3x-y-z=3 ③
①+②,得3x-z=6 ④
③-①,得2x-2z=3,
即x-z=1.5 ⑤
④-⑤,得2x=4.5
∴x=2.25
把x=2.25代入⑤,得
2.25-z=1.5
z=0.75
把x=2.25,z=0.75代入①,得
2.25-y+0.75=0
y=3
∴原方程组的解是：{x=2.25
y=3
z=0.75
a-b+c=0 (1)
4a+2b+c=3 (2)
25a+5b+c=60 (3)
(2)-(1)=3a+3b=3 (4)
(3)-(1)=24a+6b=60 (5)
(5)-2*(4)=18a=54
a=3
代入（4）b=-2
代入（1）c=-5

:x-y+z=0，2x+y-2z=6，3x-y-z=3
3x-z=6 5x-3z=9
z=3x-6 5x-9x+18=9 4x=9 x=9/4 z=27/4-6=3/4
y=9/4+3/4=3
a-b+c=0，4a+2b+c=3，25a+5b+c=60
6a+3c=3 30a+6c=60
c=1-2a 30a+6-12a=60 18a=54 a=3
c=1-6=-5 b=3-5=-2