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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:
 
12
5
A -5B = 1    (1)
-6A + 6C = 0    (2)
- 
24
5
A + 12D = 0    (3)
- 
3
8
A + 
5937
100
B - 
37
100
C - 
37
100
D = 
433
10
    (4)
Question solving process:

Multiply both sides of equation (1) by 5
Divide the two sides of equation (1) by 2, the equation can be obtained:
         6A - 
25
2
B = 
5
2
    (5)
, then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
 
12
5
A -5B = 1    (1)
- 
25
2
B + 6C = 
5
2
    (2)
- 
24
5
A + 12D = 0    (3)
- 
3
8
A + 
5937
100
B - 
37
100
C - 
37
100
D = 
433
10
    (4)

Multiply both sides of equation (1) by 2, the equation can be obtained:
         
24
5
A -10B = 2    (6)
, then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
 
12
5
A -5B = 1    (1)
- 
25
2
B + 6C = 
5
2
    (2)
-10B + 12D = 2    (3)
- 
3
8
A + 
5937
100
B - 
37
100
C - 
37
100
D = 
433
10
    (4)

Multiply both sides of equation (1) by 5
Divide the two sides of equation (1) by 32, the equation can be obtained:
         
3
8
A - 
25
32
B = 
5
32
    (7)
, then add the two sides of equation (7) to both sides of equation (4), the equations are reduced to:
 
12
5
A -5B = 1    (1)
- 
25
2
B + 6C = 
5
2
    (2)
-10B + 12D = 2    (3)
 
46871
800
B - 
37
100
C - 
37
100
D = 
6953
160
    (4)

Multiply both sides of equation (2) by 4
Divide the two sides of equation (2) by 5, the equation can be obtained:
        -10B + 
24
5
C = 2    (8)
, then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
 
12
5
A -5B = 1    (1)
- 
25
2
B + 6C = 
5
2
    (2)
- 
24
5
C + 12D = 0    (3)
 
46871
800
B - 
37
100
C - 
37
100
D = 
6953
160
    (4)

Multiply both sides of equation (2) by 46871
Divide the two sides of equation (2) by 10000, the equation can be obtained:
        - 
46871
800
B + 
140613
5000
C = 
46871
4000
    (9)
, then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
 
12
5
A -5B = 1    (1)
- 
25
2
B + 6C = 
5
2
    (2)
- 
24
5
C + 12D = 0    (3)
 
138763
5000
C - 
37
100
D = 
27587
500
    (4)

Multiply both sides of equation (3) by 138763
Divide the two sides of equation (3) by 24000, the equation can be obtained:
        - 
138763
5000
C + 
138763
2000
D = 0    (10)
, then add the two sides of equation (10) to both sides of equation (4), the equations are reduced to:
 
12
5
A -5B = 1    (1)
- 
25
2
B + 6C = 
5
2
    (2)
- 
24
5
C + 12D = 0    (3)
 
138023
2000
D = 
27587
500
    (4)

Multiply both sides of equation (4) by 24000
Divide both sides of equation (4) by 138023, get the equation：
         
4236
353
D = 
1324176
138023
    (11)
, then subtract both sides of equation (11) from both sides of equation (3), get the equation：
 
12
5
A -5B = 1    (1)
- 
25
2
B + 6C = 
5
2
    (2)
- 
24
5
C = - 
1324176
138023
    (3)
 
138023
2000
D = 
27587
500
    (4)

Multiply both sides of equation (3) by 5
Divide both sides of equation (3) by 4, get the equation：
        -6C = - 
1655220
138023
    (12)
, then add the two sides of equation (12) to both sides of equation (2), get the equation：
 
12
5
A -5B = 1    (1)
- 
25
2
B = - 
2620325
276046
    (2)
- 
24
5
C = - 
1324176
138023
    (3)
 D = 
110348
138023
    (4)

Multiply both sides of equation (2) by 2
Divide both sides of equation (2) by 5, get the equation：
        -5B = - 
524065
138023
    (13)
, then subtract both sides of equation (13) from both sides of equation (1), get the equation：
 
12
5
A = 
662088
138023
    (1)
- 
25
2
B = - 
2620325
276046
    (2)
 C = 
275870
138023
    (3)
 D = 
110348
138023
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
275870
138023
    (1)
 B = 
104813
138023
    (2)
 C = 
275870
138023
    (3)
 D = 
110348
138023
    (4)


Therefore, the solution of the equation set is:
A = 
275870
138023
B = 
104813
138023
C = 
275870
138023
D = 
110348
138023


Convert the solution of the equation set to decimals:
A = 1.998725
B = 0.759388
C = 1.998725
D = 0.799490

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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