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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:
 3A + 4B + C -1D = 0    (1)
 A -3B + 10C -1D = 0    (2)
 7A -1B + 8C -1D = 0    (3)
 A + B + C = 1    (4)
Question solving process:

Divide the two sides of equation (1) by 3, the equation can be obtained:
         A + 
4
3
B + 
1
3
C - 
1
3
D = 0    (5)
, then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
 3A + 4B + C -1D = 0    (1)
- 
13
3
B + 
29
3
C - 
2
3
D = 0    (2)
 7A -1B + 8C -1D = 0    (3)
 A + B + C = 1    (4)

Multiply both sides of equation (1) by 7
Divide the two sides of equation (1) by 3, the equation can be obtained:
         7A + 
28
3
B + 
7
3
C - 
7
3
D = 0    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 3A + 4B + C -1D = 0    (1)
- 
13
3
B + 
29
3
C - 
2
3
D = 0    (2)
- 
31
3
B + 
17
3
C + 
4
3
D = 0    (3)
 A + B + C = 1    (4)

Divide the two sides of equation (1) by 3, the equation can be obtained:
         A + 
4
3
B + 
1
3
C - 
1
3
D = 0    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 3A + 4B + C -1D = 0    (1)
- 
13
3
B + 
29
3
C - 
2
3
D = 0    (2)
- 
31
3
B + 
17
3
C + 
4
3
D = 0    (3)
- 
1
3
B + 
2
3
C + 
1
3
D = 1    (4)

Multiply both sides of equation (2) by 31
Divide the two sides of equation (2) by 13, the equation can be obtained:
        - 
31
3
B + 
899
39
C - 
62
39
D = 0    (8)
, then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
 3A + 4B + C -1D = 0    (1)
- 
13
3
B + 
29
3
C - 
2
3
D = 0    (2)
- 
226
13
C + 
38
13
D = 0    (3)
- 
1
3
B + 
2
3
C + 
1
3
D = 1    (4)

Divide the two sides of equation (2) by 13, the equation can be obtained:
        - 
1
3
B + 
29
39
C - 
2
39
D = 0    (9)
, then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
 3A + 4B + C -1D = 0    (1)
- 
13
3
B + 
29
3
C - 
2
3
D = 0    (2)
- 
226
13
C + 
38
13
D = 0    (3)
- 
1
13
C + 
5
13
D = 1    (4)

Divide the two sides of equation (3) by 226, the equation can be obtained:
        - 
113
1469
C + 
19
1469
D = 0    (10)
, then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
 3A + 4B + C -1D = 0    (1)
- 
13
3
B + 
29
3
C - 
2
3
D = 0    (2)
- 
226
13
C + 
38
13
D = 0    (3)
 
42
113
D = 
113
113
    (4)

Multiply both sides of equation (4) by 2147
Divide both sides of equation (4) by 273, get the equation：
         
4294
1469
D = 
2147
273
    (11)
, then subtract both sides of equation (11) from both sides of equation (3), get the equation：
 3A + 4B + C -1D = 0    (1)
- 
13
3
B + 
29
3
C - 
2
3
D = 0    (2)
- 
226
13
C = - 
2147
273
    (3)
 
42
113
D = 
113
113
    (4)

Multiply both sides of equation (4) by 113
Divide both sides of equation (4) by 63, get the equation：
         
226
339
D = 
12769
7119
    (12)
, then add the two sides of equation (12) to both sides of equation (2), get the equation：
 3A + 4B + C -1D = 0    (1)
- 
13
3
B + 
29
3
C = 
12769
7119
    (2)
- 
226
13
C = - 
2147
273
    (3)
 
42
113
D = 
113
113
    (4)

Multiply both sides of equation (4) by 113
Divide both sides of equation (4) by 42, get the equation：
         D = 
12769
4746
    (13)
, then add the two sides of equation (13) to both sides of equation (1), get the equation：
 3A + 4B + C = 
12769
4746
    (1)
- 
13
3
B + 
29
3
C = 
12769
7119
    (2)
- 
226
13
C = - 
2147
273
    (3)
 
42
113
D = 
113
113
    (4)

Multiply both sides of equation (3) by 377
Divide both sides of equation (3) by 678, get the equation：
        - 
3277
339
C = - 
551
126
    (14)
, then add the two sides of equation (14) to both sides of equation (2), get the equation：
 3A + 4B + C = 
12769
4746
    (1)
- 
13
3
B = - 
325
126
    (2)
- 
226
13
C = - 
2147
273
    (3)
 D = 
12769
4746
    (4)

Multiply both sides of equation (3) by 13
Divide both sides of equation (3) by 226, get the equation：
        - 
113
113
C = - 
2147
4746
    (15)
, then add the two sides of equation (15) to both sides of equation (1), get the equation：
 3A + 4B = 
5311
2373
    (1)
- 
13
3
B = - 
325
126
    (2)
- 
226
13
C = - 
2147
273
    (3)
 D = 
12769
4746
    (4)

Multiply both sides of equation (2) by 12
Divide both sides of equation (2) by 13, get the equation：
        -4B = - 
50
21
    (16)
, then add the two sides of equation (16) to both sides of equation (1), get the equation：
 3A = - 
113
791
    (1)
- 
13
3
B = - 
325
126
    (2)
 C = 
2147
4746
    (3)
 D = 
12769
4746
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = - 
113
2373
    (1)
 B = 
25
42
    (2)
 C = 
2147
4746
    (3)
 D = 
12769
4746
    (4)


Therefore, the solution of the equation set is:
A = - 
113
2373
B = 
25
42
C = 
2147
4746
D = 
12769
4746


Convert the solution of the equation set to decimals:
A = -0.047619
B = 0.595238
C = 0.452381
D = 2.690476

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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