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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:
 
125
2
x + 
5
2
y + 
1
10
z = 0    (1)
 250x + 5y + 
1
10
z = 
1
10
    (2)
 
5621
10
x + 
71
10
y + 
1
10
z = 
1
10
    (3)
Question solving process:

Multiply both sides of equation (1) by 4, the equation can be obtained:
         250x + 10y + 
2
5
z = 0    (4)
, then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
 
125
2
x + 
5
2
y + 
1
10
z = 0    (1)
-5y - 
3
10
z = 
1
10
    (2)
 
5621
10
x + 
71
10
y + 
1
10
z = 
1
10
    (3)

Multiply both sides of equation (1) by 5621
Divide the two sides of equation (1) by 625, the equation can be obtained:
         
5621
10
x + 
5621
250
y + 
5621
6250
z = 0    (5)
, then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 
125
2
x + 
5
2
y + 
1
10
z = 0    (1)
-5y - 
3
10
z = 
1
10
    (2)
- 
1923
125
y - 
2498
3125
z = 
1
10
    (3)

Multiply both sides of equation (2) by 1923
Divide the two sides of equation (2) by 625, the equation can be obtained:
        - 
1923
125
y - 
5769
6250
z = 
1923
6250
    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 
125
2
x + 
5
2
y + 
1
10
z = 0    (1)
-5y - 
3
10
z = 
1
10
    (2)
 
773
6250
z = - 
649
3125
    (3)

Multiply both sides of equation (3) by 1875
Divide both sides of equation (3) by 773, get the equation：
         
2319
7730
z = - 
1947
3865
    (7)
, then add the two sides of equation (7) to both sides of equation (2), get the equation：
 
125
2
x + 
5
2
y + 
1
10
z = 0    (1)
-5y = - 
3121
7730
    (2)
 
773
6250
z = - 
649
3125
    (3)

Multiply both sides of equation (3) by 625
Divide both sides of equation (3) by 773, get the equation：
         
773
7730
z = - 
649
3865
    (8)
, then subtract both sides of equation (8) from both sides of equation (1), get the equation：
 
125
2
x + 
5
2
y = 
649
3865
    (1)
-5y = - 
3121
7730
    (2)
 
773
6250
z = - 
649
3125
    (3)

Divide both sides of equation (2) by 2, get the equation：
        - 
5
2
y = - 
3121
15460
    (9)
, then add the two sides of equation (9) to both sides of equation (1), get the equation：
 
125
2
x = - 
81165
2390116
    (1)
-5y = - 
3121
7730
    (2)
 z = - 
1298
773
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = - 
16233
29876450
    (1)
 y = 
3121
38650
    (2)
 z = - 
1298
773
    (3)


Therefore, the solution of the equation set is:
x = - 
16233
29876450
y = 
3121
38650
z = - 
1298
773


Convert the solution of the equation set to decimals:
x = -0.000543
y = 0.080750
z = -1.679172

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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