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On line solution of multivariate equations：
    First set the elements of the equation (i.e. the number of unknowns), then click the "Next" button to enter the coefficients of each element of the equation set, and click the "Next" button to obtain the solution of the equation set.
    Note that the coefficients of each element of the equation system can only be numbers, not algebraic expressions (including mathematical functions).
    Current location：Equations > Multivariate equations > Answer
detailed information：
The input equation set is:
 
67
10
x + 
21
5
y = 
24857
20
    (1)
 
21
5
x - 
11
5
z = 
1776
5
    (2)
 
21
5
y + 
31
5
z = 
5681
5
    (3)
Question solving process:

Multiply both sides of equation (1) by 42
Divide the two sides of equation (1) by 67, the equation can be obtained:
         
21
5
x + 
882
335
y = 
7791
10
    (4)
, then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
 
67
10
x + 
21
5
y = 
24857
20
    (1)
- 
882
335
y - 
737
335
z = - 
4239
10
    (2)
 
21
5
y + 
31
5
z = 
5681
5
    (3)

Multiply both sides of equation (2) by 67
Divide the two sides of equation (2) by 42, the equation can be obtained:
        - 
21
5
y - 
737
210
z = - 
94671
140
    (5)
, then add the two sides of equation (5) to both sides of equation (3), the equations are reduced to:
 
67
10
x + 
21
5
y = 
24857
20
    (1)
- 
882
335
y - 
737
335
z = - 
4239
10
    (2)
 
113
42
z = 
64397
140
    (3)

Multiply both sides of equation (3) by 30954
Divide both sides of equation (3) by 37855, get the equation：
         
1243
565
z = 
2125101
5650
    (6)
, then add the two sides of equation (6) to both sides of equation (2), get the equation：
 
67
10
x + 
21
5
y = 
24857
20
    (1)
- 
882
335
y = - 
134967
2825
    (2)
 
113
42
z = 
64397
140
    (3)

Multiply both sides of equation (2) by 67
Divide both sides of equation (2) by 42, get the equation：
        - 
21
5
y = - 
430609
5650
    (7)
, then add the two sides of equation (7) to both sides of equation (1), get the equation：
 
67
10
x = 
13182987
11300
    (1)
- 
882
335
y = - 
134967
2825
    (2)
 z = 
193191
1130
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = 
196761
1130
    (1)
 y = 
430609
23730
    (2)
 z = 
193191
1130
    (3)


Therefore, the solution of the equation set is:
x = 
196761
1130
y = 
430609
23730
z = 
193191
1130


Convert the solution of the equation set to decimals:
x = 174.124779
y = 18.146186
z = 170.965487

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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