Question

解三元一次方程组:x-y+z=0,2x+y-2z=6

Answer 1

{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