Question

三元一次方程！急死我了！！

1、x+y=2
y+z=-3
z+x=5
2、x+y=3
2x-3y-z=5
x-2y+z=-2
3、已知x+2y=3z,3x-y=4z.求x与y之比
4、x+y=7
y+z=3
z+x-2=0
过程！答案我有。好的话追加

Answer 1

1. x+y=2 ~(1)
y+z=-3 ~ (2)
z+x=5 ~ (3)
(1)+(2)+(3): 2(x+y+z)=4
x+y+z=2 ~ (4)

(4)-(1): z=0
(4)-(2): x=5
(4)-(3): y=-3

2. x+y=3 ~ (1)
2x-3y-z=5 ~ (2)
x-2y+z=-2 ~ (3)
(2)+(3): 3x-5y=3 ~ (4)
(1)*3: 3x+3y=9 ~ (5)
(5)-(4): 8y=6
y=3/4
代y=3/4入(1): x+3/4=3
x=9/4

代x=9/4, y=3/4入(3): 9/4 - 2*3/4 + z = -2
z=-11/4

(3) x+2y=3z ~ (1)
3x-y=4z.~ (2)
(1)/(2): (x+2y)/(3x-y)=3/4
4(x+2y)=3(3x-y)
4x+8y=9x-3y
5x=11y
x:y = 11:5

4. 类似题1的做法:
x+y=7 ~ (1)
y+z=3 ~ (2)
z+x-2=0 ~ (3)
(3): z+x=2 ~ (4)
(1)+(2)+(4): 2(x+y+z)=12
x+y+z=6 ~ (5)
(5)-(1):z=-1
(5)-(2):x=3
(5)-(4):y=4