解三元一次方程组:x+y-z=0 ① 3x+y=6 ① 2x-y+3z=2 ② x+2y-z=5 ② x-4y-2z+6=0 ③ 5x-3y+2z=4 ③x+y+z=-1 ① 2x+3y=5 ①4x-2y+3z=5 ② 3y-4z=3 ②y-z=8-2x ③ 4z+5x=7 ③
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/26 03:12:40
![解三元一次方程组:x+y-z=0 ① 3x+y=6 ① 2x-y+3z=2 ② x+2y-z=5 ② x-4y-2z+6=0 ③ 5x-3y+2z=4 ③x+y+z=-1 ① 2x+3y=5 ①4x-2y+3z=5 ② 3y-4z=3 ②y-z=8-2x ③ 4z+5x=7 ③](/uploads/image/z/173188-28-8.jpg?t=%E8%A7%A3%E4%B8%89%E5%85%83%E4%B8%80%E6%AC%A1%E6%96%B9%E7%A8%8B%E7%BB%84%EF%BC%9Ax%2By-z%3D0+%E2%91%A0+3x%2By%3D6+%E2%91%A0+2x-y%2B3z%3D2+%E2%91%A1+x%2B2y-z%3D5+%E2%91%A1+x-4y-2z%2B6%3D0+%E2%91%A2+5x-3y%2B2z%3D4+%E2%91%A2x%2By%2Bz%3D-1+%E2%91%A0+2x%2B3y%3D5+%E2%91%A04x-2y%2B3z%3D5+%E2%91%A1+3y-4z%3D3+%E2%91%A1y-z%3D8-2x+%E2%91%A2+4z%2B5x%3D7+%E2%91%A2)
解三元一次方程组:x+y-z=0 ① 3x+y=6 ① 2x-y+3z=2 ② x+2y-z=5 ② x-4y-2z+6=0 ③ 5x-3y+2z=4 ③x+y+z=-1 ① 2x+3y=5 ①4x-2y+3z=5 ② 3y-4z=3 ②y-z=8-2x ③ 4z+5x=7 ③
解三元一次方程组:x+y-z=0 ① 3x+y=6 ① 2x-y+3z=2 ② x+2y-z=5 ② x-4y-2z+6=0 ③ 5x-3y+2z=4 ③
x+y+z=-1 ① 2x+3y=5 ①
4x-2y+3z=5 ② 3y-4z=3 ②
y-z=8-2x ③ 4z+5x=7 ③
解三元一次方程组:x+y-z=0 ① 3x+y=6 ① 2x-y+3z=2 ② x+2y-z=5 ② x-4y-2z+6=0 ③ 5x-3y+2z=4 ③x+y+z=-1 ① 2x+3y=5 ①4x-2y+3z=5 ② 3y-4z=3 ②y-z=8-2x ③ 4z+5x=7 ③
(1)题的过程:
由x+y-z=0可得z=x+y,代入剩余两个方程可得:2x-y+3(x+y)=2,x-4y-2(x+y)+6=0,整理得:5x+2y=2,
x+6y=6(这个式子可以两边同乘5得:5x+30y=30),由5x+2y=2,5x+30y=30两式相减消去5x,可得28y=28,y=1,再由x+6y=6(或5x+2y=2)可得x=0,而z=x+y=1,解完!详细过程就是这样,参照着做就可以了,写了这么多,其他三个方程直接给出答案:(2) x=2,y=0,z=-3; (3)x=3,y=-1,z=-3;
(4)x=5/3,y=5/9,z=-1/3;
x+y+z=-1 ①
4x-2y+3z=5 ②
y-z=8-2x ③
①×2+②得:6x+5z=3 (4)
①-③得:-x+2z=-9 (5)
(4)+(5)×6得:17z=-51,z=-3
代入(5)解得:x=3
把它们代入(1)解得:y=-1
所以,方程组的解是...
全部展开
x+y+z=-1 ①
4x-2y+3z=5 ②
y-z=8-2x ③
①×2+②得:6x+5z=3 (4)
①-③得:-x+2z=-9 (5)
(4)+(5)×6得:17z=-51,z=-3
代入(5)解得:x=3
把它们代入(1)解得:y=-1
所以,方程组的解是:
x=3
y=-1
z=-3
2x+3y=5 ①
3y-4z=3 ②
4z+5x=7 ③
①-②得:2x+4z=2 (4)
③-(4)得:3x=5,x=5/3
代入①解得:y=5/9
代入③解得:z=-1/3
所以,原方程组的解是:
x=5/3
y=5/9
z=-1/3
收起