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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:
 
13
20
A - 
1
5
B - 
1
5
C - 
1
5
D = -2    (1)
- 
1
5
A + 
6
5
B - 
1
5
D = 4    (2)
- 
1
5
A + 
1
5
C - 
1
5
D = -2    (3)
- 
1
5
A - 
1
5
B - 
1
5
C + 
6
5
D = 0    (4)
Question solving process:

Multiply both sides of equation (1) by 4
Divide the two sides of equation (1) by 13, the equation can be obtained:
         
1
5
A - 
4
65
B - 
4
65
C - 
4
65
D = - 
8
13
    (5)
, then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
 
13
20
A - 
1
5
B - 
1
5
C - 
1
5
D = -2    (1)
 
74
65
B - 
4
65
C - 
17
65
D = 
44
13
    (2)
- 
1
5
A + 
1
5
C - 
1
5
D = -2    (3)
- 
1
5
A - 
1
5
B - 
1
5
C + 
6
5
D = 0    (4)

Multiply both sides of equation (1) by 4
Divide the two sides of equation (1) by 13, the equation can be obtained:
         
1
5
A - 
4
65
B - 
4
65
C - 
4
65
D = - 
8
13
    (6)
, then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
 
13
20
A - 
1
5
B - 
1
5
C - 
1
5
D = -2    (1)
 
74
65
B - 
4
65
C - 
17
65
D = 
44
13
    (2)
- 
4
65
B + 
9
65
C - 
17
65
D = - 
34
13
    (3)
- 
1
5
A - 
1
5
B - 
1
5
C + 
6
5
D = 0    (4)

Multiply both sides of equation (1) by 4
Divide the two sides of equation (1) by 13, the equation can be obtained:
         
1
5
A - 
4
65
B - 
4
65
C - 
4
65
D = - 
8
13
    (7)
, then add the two sides of equation (7) to both sides of equation (4), the equations are reduced to:
 
13
20
A - 
1
5
B - 
1
5
C - 
1
5
D = -2    (1)
 
74
65
B - 
4
65
C - 
17
65
D = 
44
13
    (2)
- 
4
65
B + 
9
65
C - 
17
65
D = - 
34
13
    (3)
- 
17
65
B - 
17
65
C + 
74
65
D = - 
8
13
    (4)

Multiply both sides of equation (2) by 2
Divide the two sides of equation (2) by 37, the equation can be obtained:
         
4
65
B - 
8
2405
C - 
34
2405
D = 
88
481
    (8)
, then add the two sides of equation (8) to both sides of equation (3), the equations are reduced to:
 
13
20
A - 
1
5
B - 
1
5
C - 
1
5
D = -2    (1)
 
74
65
B - 
4
65
C - 
17
65
D = 
44
13
    (2)
 
5
37
C - 
51
185
D = - 
90
37
    (3)
- 
17
65
B - 
17
65
C + 
74
65
D = - 
8
13
    (4)

Multiply both sides of equation (2) by 17
Divide the two sides of equation (2) by 74, the equation can be obtained:
         
17
65
B - 
34
2405
C - 
289
4810
D = 
374
481
    (9)
, then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
 
13
20
A - 
1
5
B - 
1
5
C - 
1
5
D = -2    (1)
 
74
65
B - 
4
65
C - 
17
65
D = 
44
13
    (2)
 
5
37
C - 
51
185
D = - 
90
37
    (3)
- 
51
185
C + 
399
370
D = 
6
37
    (4)

Multiply both sides of equation (3) by 51
Divide the two sides of equation (3) by 25, the equation can be obtained:
         
51
185
C - 
2601
4625
D = - 
918
185
    (10)
, then add the two sides of equation (10) to both sides of equation (4), the equations are reduced to:
 
13
20
A - 
1
5
B - 
1
5
C - 
1
5
D = -2    (1)
 
74
65
B - 
4
65
C - 
17
65
D = 
44
13
    (2)
 
5
37
C - 
51
185
D = - 
90
37
    (3)
 
129
250
D = - 
888
185
    (4)

Multiply both sides of equation (4) by 850
Divide both sides of equation (4) by 1591, get the equation：
         
51
185
D = - 
4080
1591
    (11)
, then add the two sides of equation (11) to both sides of equation (3), get the equation：
 
13
20
A - 
1
5
B - 
1
5
C - 
1
5
D = -2    (1)
 
74
65
B - 
4
65
C - 
17
65
D = 
44
13
    (2)
 
5
37
C = - 
7950
1591
    (3)
 
129
250
D = - 
888
185
    (4)

Multiply both sides of equation (4) by 850
Divide both sides of equation (4) by 1677, get the equation：
         
17
65
D = - 
1360
559
    (12)
, then add the two sides of equation (12) to both sides of equation (2), get the equation：
 
13
20
A - 
1
5
B - 
1
5
C - 
1
5
D = -2    (1)
 
74
65
B - 
4
65
C = 
532
559
    (2)
 
5
37
C = - 
7950
1591
    (3)
 
129
250
D = - 
888
185
    (4)

Multiply both sides of equation (4) by 50
Divide both sides of equation (4) by 129, get the equation：
         
1
5
D = - 
80
43
    (13)
, then add the two sides of equation (13) to both sides of equation (1), get the equation：
 
13
20
A - 
1
5
B - 
1
5
C = - 
166
43
    (1)
 
74
65
B - 
4
65
C = 
532
559
    (2)
 
5
37
C = - 
7950
1591
    (3)
 
129
250
D = - 
888
185
    (4)

Multiply both sides of equation (3) by 148
Divide both sides of equation (3) by 325, get the equation：
         
4
65
C = - 
1272
559
    (14)
, then add the two sides of equation (14) to both sides of equation (2), get the equation：
 
13
20
A - 
1
5
B - 
1
5
C = - 
166
43
    (1)
 
74
65
B = - 
740
559
    (2)
 
5
37
C = - 
7950
1591
    (3)
 D = - 
400
43
    (4)

Multiply both sides of equation (3) by 37
Divide both sides of equation (3) by 25, get the equation：
         
1
5
C = - 
318
43
    (15)
, then add the two sides of equation (15) to both sides of equation (1), get the equation：
 
13
20
A - 
1
5
B = - 
484
43
    (1)
 
74
65
B = - 
740
559
    (2)
 
5
37
C = - 
7950
1591
    (3)
 D = - 
400
43
    (4)

Multiply both sides of equation (2) by 13
Divide both sides of equation (2) by 74, get the equation：
         
1
5
B = - 
10
43
    (16)
, then add the two sides of equation (16) to both sides of equation (1), get the equation：
 
13
20
A = - 
494
43
    (1)
 
74
65
B = - 
740
559
    (2)
 C = - 
1590
43
    (3)
 D = - 
400
43
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = - 
760
43
    (1)
 B = - 
50
43
    (2)
 C = - 
1590
43
    (3)
 D = - 
400
43
    (4)


Therefore, the solution of the equation set is:
A = - 
760
43
B = - 
50
43
C = - 
1590
43
D = - 
400
43


Convert the solution of the equation set to decimals:
A = -17.674419
B = -1.162791
C = -36.976744
D = -9.302326

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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