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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:
 35A -25B -1D = 0    (1)
-25A + 85B -50C = 230    (2)
-50B + 150C + D = 0    (3)
 
33
10
A - 
43
10
B + C = 0    (4)
Question solving process:

Multiply both sides of equation (1) by 5
Divide the two sides of equation (1) by 7, the equation can be obtained:
         25A - 
125
7
B - 
5
7
D = 0    (5)
, then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
 35A -25B -1D = 0    (1)
 
470
7
B -50C - 
5
7
D = 230    (2)
-50B + 150C + D = 0    (3)
 
33
10
A - 
43
10
B + C = 0    (4)

Multiply both sides of equation (1) by 33
Divide the two sides of equation (1) by 350, the equation can be obtained:
         
33
10
A - 
33
14
B - 
33
350
D = 0    (6)
, then subtract both sides of equation (6) from both sides of equation (4), the equations are reduced to:
 35A -25B -1D = 0    (1)
 
470
7
B -50C - 
5
7
D = 230    (2)
-50B + 150C + D = 0    (3)
- 
68
35
B + C + 
33
350
D = 0    (4)

Multiply both sides of equation (2) by 35
Divide the two sides of equation (2) by 47, the equation can be obtained:
         50B - 
1750
47
C - 
25
47
D = 
8050
47
    (7)
, then add the two sides of equation (7) to both sides of equation (3), the equations are reduced to:
 35A -25B -1D = 0    (1)
 
470
7
B -50C - 
5
7
D = 230    (2)
 
5300
47
C + 
22
47
D = 
8050
47
    (3)
- 
68
35
B + C + 
33
350
D = 0    (4)

Multiply both sides of equation (2) by 34
Divide the two sides of equation (2) by 1175, the equation can be obtained:
         
68
35
B - 
68
47
C - 
34
1645
D = 
1564
235
    (8)
, then add the two sides of equation (8) to both sides of equation (4), the equations are reduced to:
 35A -25B -1D = 0    (1)
 
470
7
B -50C - 
5
7
D = 230    (2)
 
5300
47
C + 
22
47
D = 
8050
47
    (3)
- 
21
47
C + 
173
2350
D = 
1564
235
    (4)

Multiply both sides of equation (3) by 21
Divide the two sides of equation (3) by 5300, the equation can be obtained:
         
21
47
C + 
231
124550
D = 
3381
4982
    (9)
, then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
 35A -25B -1D = 0    (1)
 
470
7
B -50C - 
5
7
D = 230    (2)
 
5300
47
C + 
22
47
D = 
8050
47
    (3)
 
188
2491
D = 
3887
530
    (4)

Multiply both sides of equation (4) by 583
Divide both sides of equation (4) by 94, get the equation：
         
1166
2491
D = 
42757
940
    (10)
, then subtract both sides of equation (10) from both sides of equation (3), get the equation：
 35A -25B -1D = 0    (1)
 
470
7
B -50C - 
5
7
D = 230    (2)
 
5300
47
C = 
118243
940
    (3)
 
188
2491
D = 
3887
530
    (4)

Multiply both sides of equation (4) by 12455
Divide both sides of equation (4) by 1316, get the equation：
         
5
7
D = 
3887
56
    (11)
, then add the two sides of equation (11) to both sides of equation (2), get the equation：
 35A -25B -1D = 0    (1)
 
470
7
B -50C = 
16767
56
    (2)
 
5300
47
C = 
118243
940
    (3)
 
188
2491
D = 
3887
530
    (4)

Multiply both sides of equation (4) by 2491
Divide both sides of equation (4) by 188, get the equation：
         D = 
206011
2120
    (12)
, then add the two sides of equation (12) to both sides of equation (1), get the equation：
 35A -25B = 
206011
2120
    (1)
 
470
7
B -50C = 
16767
56
    (2)
 
5300
47
C = 
118243
940
    (3)
 
188
2491
D = 
3887
530
    (4)

Multiply both sides of equation (3) by 47
Divide both sides of equation (3) by 106, get the equation：
         50C = 
118243
2120
    (13)
, then add the two sides of equation (13) to both sides of equation (2), get the equation：
 35A -25B = 
206011
2120
    (1)
 
470
7
B = 
24863
70
    (2)
 
5300
47
C = 
118243
940
    (3)
 D = 
206011
2120
    (4)

Multiply both sides of equation (2) by 35
Divide both sides of equation (2) by 94, get the equation：
         25B = 
529
4
    (14)
, then add the two sides of equation (14) to both sides of equation (1), get the equation：
 35A = 
486381
2120
    (1)
 
470
7
B = 
24863
70
    (2)
 C = 
2231
2000
    (3)
 D = 
206011
2120
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
1311
200
    (1)
 B = 
529
100
    (2)
 C = 
2231
2000
    (3)
 D = 
206011
2120
    (4)


Therefore, the solution of the equation set is:
A = 
1311
200
B = 
529
100
C = 
2231
2000
D = 
206011
2120


Convert the solution of the equation set to decimals:
A = 6.555000
B = 5.290000
C = 1.115500
D = 97.175000

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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