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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:
 14A + 6B + 11C -1D = 0    (1)
-2A + 12B -6C -1D = 0    (2)
-12A + 6B + 10C -1D = 0    (3)
 A + B + C = 1    (4)
Question solving process:

Divide the two sides of equation (1) by 7, the equation can be obtained:
         2A + 
6
7
B + 
11
7
C - 
1
7
D = 0    (5)
, then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
 14A + 6B + 11C -1D = 0    (1)
 
90
7
B - 
31
7
C - 
8
7
D = 0    (2)
-12A + 6B + 10C -1D = 0    (3)
 A + B + C = 1    (4)

Multiply both sides of equation (1) by 6
Divide the two sides of equation (1) by 7, the equation can be obtained:
         12A + 
36
7
B + 
66
7
C - 
6
7
D = 0    (6)
, then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
 14A + 6B + 11C -1D = 0    (1)
 
90
7
B - 
31
7
C - 
8
7
D = 0    (2)
 
78
7
B + 
136
7
C - 
13
7
D = 0    (3)
 A + B + C = 1    (4)

Divide the two sides of equation (1) by 14, the equation can be obtained:
         A + 
3
7
B + 
11
14
C - 
1
14
D = 0    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 14A + 6B + 11C -1D = 0    (1)
 
90
7
B - 
31
7
C - 
8
7
D = 0    (2)
 
78
7
B + 
136
7
C - 
13
7
D = 0    (3)
 
4
7
B + 
3
14
C + 
1
14
D = 1    (4)

Multiply both sides of equation (2) by 13
Divide the two sides of equation (2) by 15, the equation can be obtained:
         
78
7
B - 
403
105
C - 
104
105
D = 0    (8)
, then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
 14A + 6B + 11C -1D = 0    (1)
 
90
7
B - 
31
7
C - 
8
7
D = 0    (2)
 
349
15
C - 
13
15
D = 0    (3)
 
4
7
B + 
3
14
C + 
1
14
D = 1    (4)

Multiply both sides of equation (2) by 2
Divide the two sides of equation (2) by 45, the equation can be obtained:
         
4
7
B - 
62
315
C - 
16
315
D = 0    (9)
, then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
 14A + 6B + 11C -1D = 0    (1)
 
90
7
B - 
31
7
C - 
8
7
D = 0    (2)
 
349
15
C - 
13
15
D = 0    (3)
 
37
90
C + 
11
90
D = 1    (4)

Multiply both sides of equation (3) by 37
Divide the two sides of equation (3) by 2094, the equation can be obtained:
         
12913
31410
C - 
481
31410
D = 0    (10)
, then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
 14A + 6B + 11C -1D = 0    (1)
 
90
7
B - 
31
7
C - 
8
7
D = 0    (2)
 
349
15
C - 
13
15
D = 0    (3)
 
48
349
D = 
349
349
    (4)

Multiply both sides of equation (4) by 4537
Divide both sides of equation (4) by 720, get the equation：
         
4537
5235
D = 
4537
720
    (11)
, then add the two sides of equation (11) to both sides of equation (3), get the equation：
 14A + 6B + 11C -1D = 0    (1)
 
90
7
B - 
31
7
C - 
8
7
D = 0    (2)
 
349
15
C = 
4537
720
    (3)
 
48
349
D = 
349
349
    (4)

Multiply both sides of equation (4) by 349
Divide both sides of equation (4) by 42, get the equation：
         
2792
2443
D = 
121801
14658
    (12)
, then add the two sides of equation (12) to both sides of equation (2), get the equation：
 14A + 6B + 11C -1D = 0    (1)
 
90
7
B - 
31
7
C = 
121801
14658
    (2)
 
349
15
C = 
4537
720
    (3)
 
48
349
D = 
349
349
    (4)

Multiply both sides of equation (4) by 349
Divide both sides of equation (4) by 48, get the equation：
         D = 
121801
16752
    (13)
, then add the two sides of equation (13) to both sides of equation (1), get the equation：
 14A + 6B + 11C = 
121801
16752
    (1)
 
90
7
B - 
31
7
C = 
121801
14658
    (2)
 
349
15
C = 
4537
720
    (3)
 
48
349
D = 
349
349
    (4)

Multiply both sides of equation (3) by 465
Divide both sides of equation (3) by 2443, get the equation：
         
10819
2443
C = 
140647
117264
    (14)
, then add the two sides of equation (14) to both sides of equation (2), get the equation：
 14A + 6B + 11C = 
121801
16752
    (1)
 
90
7
B = 
371685
39088
    (2)
 
349
15
C = 
4537
720
    (3)
 D = 
121801
16752
    (4)

Multiply both sides of equation (3) by 165
Divide both sides of equation (3) by 349, get the equation：
         
3839
349
C = 
49907
16752
    (15)
, then subtract both sides of equation (15) from both sides of equation (1), get the equation：
 14A + 6B = 
35947
8376
    (1)
 
90
7
B = 
371685
39088
    (2)
 
349
15
C = 
4537
720
    (3)
 D = 
121801
16752
    (4)

Multiply both sides of equation (2) by 7
Divide both sides of equation (2) by 15, get the equation：
         6B = 
24779
5584
    (16)
, then subtract both sides of equation (16) from both sides of equation (1), get the equation：
 14A = - 
2443
16752
    (1)
 
90
7
B = 
371685
39088
    (2)
 C = 
4537
16752
    (3)
 D = 
121801
16752
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = - 
349
33504
    (1)
 B = 
24779
33504
    (2)
 C = 
4537
16752
    (3)
 D = 
121801
16752
    (4)


Therefore, the solution of the equation set is:
A = - 
349
33504
B = 
24779
33504
C = 
4537
16752
D = 
121801
16752


Convert the solution of the equation set to decimals:
A = -0.010417
B = 0.739583
C = 0.270833
D = 7.270833

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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