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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:
 50A + 23B + 6C + 10D = 0    (1)
 15A + 30B + 20C + 10D = 0    (2)
 90A + 50B + 60C + 10D = 0    (3)
 2A + 6B + 20C + 10D = 0    (4)
Question solving process:

Multiply both sides of equation (1) by 3
Divide the two sides of equation (1) by 10, the equation can be obtained:
         15A + 
69
10
B + 
9
5
C + 3D = 0    (5)
, then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
 50A + 23B + 6C + 10D = 0    (1)
 
231
10
B + 
91
5
C + 7D = 0    (2)
 90A + 50B + 60C + 10D = 0    (3)
 2A + 6B + 20C + 10D = 0    (4)

Multiply both sides of equation (1) by 9
Divide the two sides of equation (1) by 5, the equation can be obtained:
         90A + 
207
5
B + 
54
5
C + 18D = 0    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 50A + 23B + 6C + 10D = 0    (1)
 
231
10
B + 
91
5
C + 7D = 0    (2)
 
43
5
B + 
246
5
C -8D = 0    (3)
 2A + 6B + 20C + 10D = 0    (4)

Divide the two sides of equation (1) by 25, the equation can be obtained:
         2A + 
23
25
B + 
6
25
C + 
2
5
D = 0    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 50A + 23B + 6C + 10D = 0    (1)
 
231
10
B + 
91
5
C + 7D = 0    (2)
 
43
5
B + 
246
5
C -8D = 0    (3)
 
127
25
B + 
494
25
C + 
48
5
D = 0    (4)

Multiply both sides of equation (2) by 86
Divide the two sides of equation (2) by 231, the equation can be obtained:
         
43
5
B + 
1118
165
C + 
86
33
D = 0    (8)
, then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
 50A + 23B + 6C + 10D = 0    (1)
 
231
10
B + 
91
5
C + 7D = 0    (2)
 
1400
33
C - 
350
33
D = 0    (3)
 
127
25
B + 
494
25
C + 
48
5
D = 0    (4)

Multiply both sides of equation (2) by 254
Divide the two sides of equation (2) by 1155, the equation can be obtained:
         
127
25
B + 
3302
825
C + 
254
165
D = 0    (9)
, then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
 50A + 23B + 6C + 10D = 0    (1)
 
231
10
B + 
91
5
C + 7D = 0    (2)
 
1400
33
C - 
350
33
D = 0    (3)
 
520
33
C + 
266
33
D = 0    (4)

Multiply both sides of equation (3) by 13
Divide the two sides of equation (3) by 35, the equation can be obtained:
         
520
33
C - 
130
33
D = 0    (10)
, then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
 50A + 23B + 6C + 10D = 0    (1)
 
231
10
B + 
91
5
C + 7D = 0    (2)
 
1400
33
C - 
350
33
D = 0    (3)
 12D = 0    (4)

Multiply both sides of equation (4) by 175
Divide both sides of equation (4) by 198, get the equation：
         
350
33
D = 0    (11)
, then add the two sides of equation (11) to both sides of equation (3), get the equation：
 50A + 23B + 6C + 10D = 0    (1)
 
231
10
B + 
91
5
C + 7D = 0    (2)
 
1400
33
C = 0    (3)
 12D = 0    (4)

Multiply both sides of equation (4) by 7
Divide both sides of equation (4) by 12, get the equation：
         7D = 0    (12)
, then subtract both sides of equation (12) from both sides of equation (2), get the equation：
 50A + 23B + 6C + 10D = 0    (1)
 
231
10
B + 
91
5
C = 0    (2)
 
1400
33
C = 0    (3)
 12D = 0    (4)

Multiply both sides of equation (4) by 5
Divide both sides of equation (4) by 6, get the equation：
         10D = 0    (13)
, then subtract both sides of equation (13) from both sides of equation (1), get the equation：
 50A + 23B + 6C = 0    (1)
 
231
10
B + 
91
5
C = 0    (2)
 
1400
33
C = 0    (3)
 12D = 0    (4)

Multiply both sides of equation (3) by 429
Divide both sides of equation (3) by 1000, get the equation：
         
91
5
C = 0    (14)
, then subtract both sides of equation (14) from both sides of equation (2), get the equation：
 50A + 23B + 6C = 0    (1)
 
231
10
B = 0    (2)
 
1400
33
C = 0    (3)
 D = 0    (4)

Multiply both sides of equation (3) by 99
Divide both sides of equation (3) by 700, get the equation：
         6C = 0    (15)
, then subtract both sides of equation (15) from both sides of equation (1), get the equation：
 50A + 23B = 0    (1)
 
231
10
B = 0    (2)
 
1400
33
C = 0    (3)
 D = 0    (4)

Multiply both sides of equation (2) by 230
Divide both sides of equation (2) by 231, get the equation：
         23B = 0    (16)
, then subtract both sides of equation (16) from both sides of equation (1), get the equation：
 50A = 0    (1)
 
231
10
B = 0    (2)
 C = 0    (3)
 D = 0    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 0    (1)
 B = 0    (2)
 C = 0    (3)
 D = 0    (4)


Therefore, the solution of the equation set is:
A = 0
B = 0
C = 0
D = 0

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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