Question

求解三元一次方程

1，2x+4y+3z=9
3x-2y+5z=11
5x+6y+8z=0
2,x:y:z=1:2:3
2x+y-3z=15
3,2x+6y+3z=6
3x-12y+7y=-3
4x-3y+4z=11

Answer 1

1，2x+4y+3z=9------------------(1)
3x-2y+5z=11----------------(2)
5x+6y+8z=0-----------------(3)
(1)+(2)-(3),得-4y=20,即,y=-5
将y=-5代入(1)和(2),得
2x-20+3z=9------------->2x+3z=29
3x+10+5z=11----------->3x+5z=1
联立方程,解得x=142,z= -85
所以,方程组的解为x=142,y= -5,z= -85

2,x:y:z=1:2:3-------------(1)
2x+y-3z=15-----------(2)
由(1)知y=2x,z=3x,
将y=2x,z=3x,代入(2),得
2x+2x-9x=15,
x=-3
y=2x=2×(-3)=-6
x=3x=3×(-3)=-9
所以,方程组的解为x= -3, y= -6, z= -9

3,2x+6y+3z=6------------------(1)
3x-12y+7y=-3----------------(2)
4x-3y+4z=11-----------------(3)
(1)×2+(2),得 7x+13z=9
(3)×4-(2),得 13x+9z=47
联立方程组,得x=5, z=-2
将x=5, z=-2代入(1)
解得y=1/3
所以,方程组的解为x=5,y= 1/3 ,z= -2

Answer 2

1,2x+4y+3z=9 (1)
3x-2y+5z=11 (2)
5x+6y+8z=0 (3)
(3)-(1)-(2)消元x得:4y=-20,y=-5
代入(1)得2x+3z=29 (4)
代入(2)得3x+5z=1 (5)
(4)乘3得:6x+9z=87 (6)
(5)乘2得:6x+10z=2 (7)
(7)-(6)得: z=-85
代入(4)得:2x=29+3*85, x=142
2,x:y:z=1:2:3 (1)
2x+y-3z=15 (2)
由(1)得y=2x,z=3x,代入(2)得2x+2x-9x=15,x=-3
由(1)y=-6,z=-9
3,2x+6y+3z=6 (1)
3x-12y+7z=-3 (2)
4x-3y+4z=11 (3)
(1)*2-(3)得
15y+2z=1 (4)
(1)*3-(2)*2得
42y-5z=24 (5)
(4)*5+(5)*2得
159y=53, y=1/3
代入(4)得z=-2
代入(1)得x=5

Answer 3