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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:
 
31
10
x + 
9
5
y + z = 
14
5
    (1)
 z = 
21
10
    (2)
 
123
10
x + 
33
10
y + z = 
23
10
    (3)
Question solving process:

Multiply both sides of equation (1) by 123
Divide the two sides of equation (1) by 31, the equation can be obtained:
         
123
10
x + 
1107
155
y + 
123
31
z = 
1722
155
    (4)
, then subtract both sides of equation (4) from both sides of equation (3), the equations are reduced to:
 
31
10
x + 
9
5
y + z = 
14
5
    (1)
 z = 
21
10
    (2)
- 
1191
310
y - 
92
31
z = - 
2731
310
    (3)

交After the exchange of equation (2) and equation (3)， the equation system becomes:
 
31
10
x + 
9
5
y + z = 
14
5
    (1)
- 
1191
310
y - 
92
31
z = - 
2731
310
    (2)
 z = 
21
10
    (3)

Multiply both sides of equation (3) by 92
Divide both sides of equation (3) by 31, get the equation：
         
92
31
z = 
966
155
    (5)
, then add the two sides of equation (5) to both sides of equation (2), get the equation：
 
31
10
x + 
9
5
y + z = 
14
5
    (1)
- 
1191
310
y = - 
799
310
    (2)
 z = 
21
10
    (3)

Subtract both sides of equation (3) from both sides of equation (1), get the equation：
 
31
10
x + 
9
5
y = 
7
10
    (1)
- 
1191
310
y = - 
799
310
    (2)
 z = 
21
10
    (3)

Multiply both sides of equation (2) by 186
Divide both sides of equation (2) by 397, get the equation：
        - 
3573
1985
y = - 
2397
1985
    (6)
, then add the two sides of equation (6) to both sides of equation (1), get the equation：
 
31
10
x = - 
403
794
    (1)
- 
1191
310
y = - 
799
310
    (2)
 z = 
21
10
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = - 
65
397
    (1)
 y = 
799
1191
    (2)
 z = 
21
10
    (3)


Therefore, the solution of the equation set is:
x = - 
65
397
y = 
799
1191
z = 
21
10


Convert the solution of the equation set to decimals:
x = -0.163728
y = 0.670865
z = 2.100000

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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