Mathematics
语言：中文
Language:English

current location：Equations > Multivariate equations > Answer
Detailed information：
The input equation set is:
- 
9
10
x + 
1
10
y + 
1
5
z = - 
3
10
    (1)
- 
9
10
y + 
9
10
z = - 
9
10
    (2)
 
9
10
x -1z = - 
9
10
    (3)
Question solving process:

Add both sides of equation (1) to both sides of equation (3) ,the equations are reduced to:
- 
9
10
x + 
1
10
y + 
1
5
z = - 
3
10
    (1)
- 
9
10
y + 
9
10
z = - 
9
10
    (2)
 
1
10
y - 
4
5
z = - 
6
5
    (3)

Divide the two sides of equation (2) by 9, the equation can be obtained:
        - 
1
10
y + 
1
10
z = - 
1
10
    (4)
, then add the two sides of equation (4) to both sides of equation (3), the equations are reduced to:
- 
9
10
x + 
1
10
y + 
1
5
z = - 
3
10
    (1)
- 
9
10
y + 
9
10
z = - 
9
10
    (2)
- 
7
10
z = - 
13
10
    (3)

Multiply both sides of equation (3) by 9
Divide both sides of equation (3) by 7, get the equation：
        - 
9
10
z = - 
117
70
    (5)
, then add the two sides of equation (5) to both sides of equation (2), get the equation：
- 
9
10
x + 
1
10
y + 
1
5
z = - 
3
10
    (1)
- 
9
10
y = - 
18
7
    (2)
- 
7
10
z = - 
13
10
    (3)

Multiply both sides of equation (3) by 2
Divide both sides of equation (3) by 7, get the equation：
        - 
1
5
z = - 
13
35
    (6)
, then add the two sides of equation (6) to both sides of equation (1), get the equation：
- 
9
10
x + 
1
10
y = - 
47
70
    (1)
- 
9
10
y = - 
18
7
    (2)
- 
7
10
z = - 
13
10
    (3)

Divide both sides of equation (2) by 9, get the equation：
        - 
1
10
y = - 
2
7
    (7)
, then add the two sides of equation (7) to both sides of equation (1), get the equation：
- 
9
10
x = - 
67
70
    (1)
- 
9
10
y = - 
18
7
    (2)
 z = 
13
7
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = 
67
63
    (1)
 y = 
20
7
    (2)
 z = 
13
7
    (3)


Therefore, the solution of the equation set is:
x = 
67
63
y = 
20
7
z = 
13
7


Convert the solution of the equation set to decimals:
x = 1.063492
y = 2.857143
z = 1.857143

解方程组的详细方法请参阅：《多元一次方程组的解法》
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