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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:
 
3111
10000
A - 
1
10
C = 
1
10
    (1)
- 
1
10
C + 
1
10
E = - 
1
10
    (2)
 
1
10
B - 
1
10
C = - 
1
10
    (3)
- 
1
10
C + 
1
10
D = - 
1
10
    (4)
- 
1
10
A - 
1
10
B + 
11
10
C - 
1
10
D - 
1
10
E = - 
1
10
    (5)
Question solving process:

Multiply both sides of equation (1) by 1000
Divide the two sides of equation (1) by 3111, the equation can be obtained:
         
1
10
A - 
100
3111
C = 
100
3111
    (6)
, then add the two sides of equation (6) to both sides of equation (5), the equations are reduced to:
 
3111
10000
A - 
1
10
C = 
1
10
    (1)
- 
1
10
C + 
1
10
E = - 
1
10
    (2)
 
1
10
B - 
1
10
C = - 
1
10
    (3)
- 
1
10
C + 
1
10
D = - 
1
10
    (4)
- 
1
10
B + 
33221
31110
C - 
1
10
D - 
1
10
E = - 
2111
31110
    (5)

交After the exchange of equation (2) and equation (3)， the equation system becomes:
 
3111
10000
A - 
1
10
C = 
1
10
    (1)
 
1
10
B - 
1
10
C = - 
1
10
    (2)
- 
1
10
C + 
1
10
E = - 
1
10
    (3)
- 
1
10
C + 
1
10
D = - 
1
10
    (4)
- 
1
10
B + 
33221
31110
C - 
1
10
D - 
1
10
E = - 
2111
31110
    (5)

Add both sides of equation (2) to both sides of equation (5) ,the equations are reduced to:
 
3111
10000
A - 
1
10
C = 
1
10
    (1)
 
1
10
B - 
1
10
C = - 
1
10
    (2)
- 
1
10
C + 
1
10
E = - 
1
10
    (3)
- 
1
10
C + 
1
10
D = - 
1
10
    (4)
 
3011
3111
C - 
1
10
D - 
1
10
E = - 
2611
15555
    (5)

Subtract both sides of equation (3) from both sides of equation (4) ,the equations are reduced to:
 
3111
10000
A - 
1
10
C = 
1
10
    (1)
 
1
10
B - 
1
10
C = - 
1
10
    (2)
- 
1
10
C + 
1
10
E = - 
1
10
    (3)
 
1
10
D - 
1
10
E = 0    (4)
 
3011
3111
C - 
1
10
D - 
1
10
E = - 
2611
15555
    (5)

Multiply both sides of equation (3) by 30110
Divide the two sides of equation (3) by 3111, the equation can be obtained:
        - 
3011
3111
C + 
3011
3111
E = - 
3011
3111
    (7)
, then add the two sides of equation (7) to both sides of equation (5), the equations are reduced to:
 
3111
10000
A - 
1
10
C = 
1
10
    (1)
 
1
10
B - 
1
10
C = - 
1
10
    (2)
- 
1
10
C + 
1
10
E = - 
1
10
    (3)
 
1
10
D - 
1
10
E = 0    (4)
- 
1
10
D + 
26999
31110
E = - 
17666
15555
    (5)

Add both sides of equation (4) to both sides of equation (5) ,the equations are reduced to:
 
3111
10000
A - 
1
10
C = 
1
10
    (1)
 
1
10
B - 
1
10
C = - 
1
10
    (2)
- 
1
10
C + 
1
10
E = - 
1
10
    (3)
 
1
10
D - 
1
10
E = 0    (4)
 
11944
15555
E = - 
17666
15555
    (5)

Multiply both sides of equation (5) by 3111
Divide both sides of equation (5) by 23888, get the equation：
         
1493
14930
E = - 
8833
59720
    (8)
, then add the two sides of equation (8) to both sides of equation (4), get the equation：
 
3111
10000
A - 
1
10
C = 
1
10
    (1)
 
1
10
B - 
1
10
C = - 
1
10
    (2)
- 
1
10
C + 
1
10
E = - 
1
10
    (3)
 
1
10
D = - 
8833
59720
    (4)
 
11944
15555
E = - 
17666
15555
    (5)

Multiply both sides of equation (5) by 3111
Divide both sides of equation (5) by 23888, get the equation：
         
1493
14930
E = - 
8833
59720
    (9)
, then subtract both sides of equation (9) from both sides of equation (3), get the equation：
 
3111
10000
A - 
1
10
C = 
1
10
    (1)
 
1
10
B - 
1
10
C = - 
1
10
    (2)
- 
1
10
C = 
2861
59720
    (3)
 
1
10
D = - 
8833
59720
    (4)
 
11944
15555
E = - 
17666
15555
    (5)

Subtract both sides of equation (3) from both sides of equation (2), get the equation：
 
3111
10000
A - 
1
10
C = 
1
10
    (1)
 
1
10
B = - 
8833
59720
    (2)
- 
1
10
C = 
2861
59720
    (3)
 D = - 
8833
5972
    (4)
 E = - 
8833
5972
    (5)

Subtract both sides of equation (3) from both sides of equation (1), get the equation：
 
3111
10000
A = 
3111
59720
    (1)
 
1
10
B = - 
8833
59720
    (2)
- 
1
10
C = 
2861
59720
    (3)
 D = - 
8833
5972
    (4)
 E = - 
8833
5972
    (5)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
250
1493
    (1)
 B = - 
8833
5972
    (2)
 C = - 
2861
5972
    (3)
 D = - 
8833
5972
    (4)
 E = - 
8833
5972
    (5)


Therefore, the solution of the equation set is:
A = 
250
1493
B = - 
8833
5972
C = - 
2861
5972
D = - 
8833
5972
E = - 
8833
5972


Convert the solution of the equation set to decimals:
A = 0.167448
B = -1.479069
C = -0.479069
D = -1.479069
E = -1.479069

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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