(1)5x+y+z=6(2)x:z=7:3(6)x/3=y/6=z/8x+5y+z=-2x:y=5:33x+5y-6z=-18x+y+5z=102x-y-z=34

Question

(1)5x+y+z=6 (2)x:z=7:3 (6)x/3=y/6=z/8
x+5y+z=-2 x:y=5:3 3x+5y-6z=-18
x+y+5z=10 2x-y-z=34

Answer 1

(1)
5x+y+z=6 --------------(1)
x+5y+z=-2 --------------(2)
x+y+5z=10 ---------------(3)
(2)-(3)得：4y-4z=-12,y-z=-3 ---------------(4)
(2)*5-(1)得：24y+4z=-16,6y+z=-4 -------(5)
(4)+(5)得：7y=-7,y=-1,代入(4)得：-1-z=-3,z=-2,
y=-1,z=-2代入 (2)得：x-5-10=10,x=25
x=25,
y=-1,
z=-2
(2)
x:z=7:3 -------------------------------(1)
x:y=5:3 -----------------------------(2)
2x-y-z=34 -------------------------(3)
z=3x/7
y=3x/5
代入(3)得：2x-3x/5-3x/7=34,34x/35=34,x=35
z=3x/7=15
y=3x/5=21
x=35
(6)
x/3=y/6=z/8 ----------------------(1)
3x+5y-6z=-18 -----------------------(2)
由(1)得：y=2x,z=8x/3 代入(2)得：
3x+10x-16x=-18,x=6
y=2x=12
z=8x/3=16
x=6