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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:
 A -1B = 
3
2
    (1)
 A + 
3
10
B -1C = 
3
2
    (2)
 A + 
3
10
B + 
3
10
C -1D = 
13
10
    (3)
 A + 
3
10
B + 
3
10
C + 
3
10
D -1E = 
13
10
    (4)
 B + C + D + E = 50    (5)
Question solving process:

Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
 A -1B = 
3
2
    (1)
 
13
10
B -1C = 0    (2)
 A + 
3
10
B + 
3
10
C -1D = 
13
10
    (3)
 A + 
3
10
B + 
3
10
C + 
3
10
D -1E = 
13
10
    (4)
 B + C + D + E = 50    (5)

Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:
 A -1B = 
3
2
    (1)
 
13
10
B -1C = 0    (2)
 
13
10
B + 
3
10
C -1D = - 
1
5
    (3)
 A + 
3
10
B + 
3
10
C + 
3
10
D -1E = 
13
10
    (4)
 B + C + D + E = 50    (5)

Subtract both sides of equation (1) from both sides of equation (4) ,the equations are reduced to:
 A -1B = 
3
2
    (1)
 
13
10
B -1C = 0    (2)
 
13
10
B + 
3
10
C -1D = - 
1
5
    (3)
 
13
10
B + 
3
10
C + 
3
10
D -1E = - 
1
5
    (4)
 B + C + D + E = 50    (5)

Subtract both sides of equation (2) from both sides of equation (3) ,the equations are reduced to:
 A -1B = 
3
2
    (1)
 
13
10
B -1C = 0    (2)
 
13
10
C -1D = - 
1
5
    (3)
 
13
10
B + 
3
10
C + 
3
10
D -1E = - 
1
5
    (4)
 B + C + D + E = 50    (5)

Subtract both sides of equation (2) from both sides of equation (4) ,the equations are reduced to:
 A -1B = 
3
2
    (1)
 
13
10
B -1C = 0    (2)
 
13
10
C -1D = - 
1
5
    (3)
 
13
10
C + 
3
10
D -1E = - 
1
5
    (4)
 B + C + D + E = 50    (5)

Multiply both sides of equation (2) by 10
Divide the two sides of equation (2) by 13, the equation can be obtained:
         B - 
10
13
C = 0    (6)
, then subtract both sides of equation (6) from both sides of equation (5), the equations are reduced to:
 A -1B = 
3
2
    (1)
 
13
10
B -1C = 0    (2)
 
13
10
C -1D = - 
1
5
    (3)
 
13
10
C + 
3
10
D -1E = - 
1
5
    (4)
 
23
13
C + D + E = 50    (5)

Subtract both sides of equation (3) from both sides of equation (4) ,the equations are reduced to:
 A -1B = 
3
2
    (1)
 
13
10
B -1C = 0    (2)
 
13
10
C -1D = - 
1
5
    (3)
 
13
10
D -1E = 0    (4)
 
23
13
C + D + E = 50    (5)

Multiply both sides of equation (3) by 230
Divide the two sides of equation (3) by 169, the equation can be obtained:
         
23
13
C - 
230
169
D = - 
46
169
    (7)
, then subtract both sides of equation (7) from both sides of equation (5), the equations are reduced to:
 A -1B = 
3
2
    (1)
 
13
10
B -1C = 0    (2)
 
13
10
C -1D = - 
1
5
    (3)
 
13
10
D -1E = 0    (4)
 
399
169
D + E = 
8496
169
    (5)

Multiply both sides of equation (4) by 3990
Divide the two sides of equation (4) by 2197, the equation can be obtained:
         
399
169
D - 
3990
2197
E = 0    (8)
, then subtract both sides of equation (8) from both sides of equation (5), the equations are reduced to:
 A -1B = 
3
2
    (1)
 
13
10
B -1C = 0    (2)
 
13
10
C -1D = - 
1
5
    (3)
 
13
10
D -1E = 0    (4)
 
6187
2197
E = 
8496
169
    (5)

Multiply both sides of equation (5) by 2197
Divide both sides of equation (5) by 6187, get the equation：
         E = 
110448
6187
    (9)
, then add the two sides of equation (9) to both sides of equation (4), get the equation：
 A -1B = 
3
2
    (1)
 
13
10
B -1C = 0    (2)
 
13
10
C -1D = - 
1
5
    (3)
 
13
10
D = 
110448
6187
    (4)
 
6187
2197
E = 
8496
169
    (5)

Multiply both sides of equation (4) by 10
Divide both sides of equation (4) by 13, get the equation：
         D = 
84960
6187
    (10)
, then add the two sides of equation (10) to both sides of equation (3), get the equation：
 A -1B = 
3
2
    (1)
 
13
10
B -1C = 0    (2)
 
13
10
C = 
418613
30935
    (3)
 
13
10
D = 
110448
6187
    (4)
 E = 
110448
6187
    (5)

Multiply both sides of equation (3) by 10
Divide both sides of equation (3) by 13, get the equation：
         C = 
64402
6187
    (11)
, then add the two sides of equation (11) to both sides of equation (2), get the equation：
 A -1B = 
3
2
    (1)
 
13
10
B = 
64402
6187
    (2)
 
13
10
C = 
418613
30935
    (3)
 D = 
84960
6187
    (4)
 E = 
110448
6187
    (5)

Multiply both sides of equation (2) by 10
Divide both sides of equation (2) by 13, get the equation：
         B = 
49540
6187
    (12)
, then add the two sides of equation (12) to both sides of equation (1), get the equation：
 A = 
117641
12374
    (1)
 
13
10
B = 
64402
6187
    (2)
 C = 
64402
6187
    (3)
 D = 
84960
6187
    (4)
 E = 
110448
6187
    (5)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
117641
12374
    (1)
 B = 
49540
6187
    (2)
 C = 
64402
6187
    (3)
 D = 
84960
6187
    (4)
 E = 
110448
6187
    (5)


Therefore, the solution of the equation set is:
A = 
117641
12374
B = 
49540
6187
C = 
64402
6187
D = 
84960
6187
E = 
110448
6187


Convert the solution of the equation set to decimals:
A = 9.507112
B = 8.007112
C = 10.409245
D = 13.732019
E = 17.851624

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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