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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:
 A + B + C = 
83683
50
    (1)
 
54
5
A + 
83
10
B + D = 
102093
10
    (2)
 
23
10
A + 
53
10
B + 
133
10
C -1D = 
123853
10
    (3)
 
23
10
B + 
103
10
C -1D = 
78663
10
    (4)
Question solving process:

Multiply both sides of equation (1) by 54
Divide the two sides of equation (1) by 5, the equation can be obtained:
         
54
5
A + 
54
5
B + 
54
5
C = 
2259441
125
    (5)
, then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
 A + B + C = 
83683
50
    (1)
- 
5
2
B - 
54
5
C + D = - 
1966557
250
    (2)
 
23
10
A + 
53
10
B + 
133
10
C -1D = 
123853
10
    (3)
 
23
10
B + 
103
10
C -1D = 
78663
10
    (4)

Multiply both sides of equation (1) by 23
Divide the two sides of equation (1) by 10, the equation can be obtained:
         
23
10
A + 
23
10
B + 
23
10
C = 
1924709
500
    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 A + B + C = 
83683
50
    (1)
- 
5
2
B - 
54
5
C + D = - 
1966557
250
    (2)
 3B + 11C -1D = 
4267941
500
    (3)
 
23
10
B + 
103
10
C -1D = 
78663
10
    (4)

Multiply both sides of equation (2) by 6
Divide the two sides of equation (2) by 5, the equation can be obtained:
        -3B - 
324
25
C + 
6
5
D = - 
5899671
625
    (7)
, then add the two sides of equation (7) to both sides of equation (3), the equations are reduced to:
 A + B + C = 
83683
50
    (1)
- 
5
2
B - 
54
5
C + D = - 
1966557
250
    (2)
- 
49
25
C + 
1
5
D = - 
2258979
2500
    (3)
 
23
10
B + 
103
10
C -1D = 
78663
10
    (4)

Multiply both sides of equation (2) by 23
Divide the two sides of equation (2) by 25, the equation can be obtained:
        - 
23
10
B - 
1242
125
C + 
23
25
D = - 
45230811
6250
    (8)
, then add the two sides of equation (8) to both sides of equation (4), the equations are reduced to:
 A + B + C = 
83683
50
    (1)
- 
5
2
B - 
54
5
C + D = - 
1966557
250
    (2)
- 
49
25
C + 
1
5
D = - 
2258979
2500
    (3)
 
91
250
C - 
2
25
D = 
1966782
3125
    (4)

Multiply both sides of equation (3) by 13
Divide the two sides of equation (3) by 70, the equation can be obtained:
        - 
91
250
C + 
13
350
D = - 
29366727
175000
    (9)
, then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
 A + B + C = 
83683
50
    (1)
- 
5
2
B - 
54
5
C + D = - 
1966557
250
    (2)
- 
49
25
C + 
1
5
D = - 
2258979
2500
    (3)
- 
3
70
D = 
16154613
35000
    (4)

Multiply both sides of equation (4) by 14
Divide both sides of equation (4) by 3, get the equation：
        - 
1
5
D = 
5384871
2500
    (10)
, then add the two sides of equation (10) to both sides of equation (3), get the equation：
 A + B + C = 
83683
50
    (1)
- 
5
2
B - 
54
5
C + D = - 
1966557
250
    (2)
- 
49
25
C = 
781473
625
    (3)
- 
3
70
D = 
16154613
35000
    (4)

Multiply both sides of equation (4) by 70
Divide both sides of equation (4) by 3, get the equation：
        -1D = 
5384871
500
    (11)
, then add the two sides of equation (11) to both sides of equation (2), get the equation：
 A + B + C = 
83683
50
    (1)
- 
5
2
B - 
54
5
C = 
1451757
500
    (2)
- 
49
25
C = 
781473
625
    (3)
- 
3
70
D = 
16154613
35000
    (4)

Multiply both sides of equation (3) by 270
Divide both sides of equation (3) by 49, get the equation：
        - 
54
5
C = 
6028506
875
    (12)
, then subtract both sides of equation (12) from both sides of equation (2), get the equation：
 A + B + C = 
83683
50
    (1)
- 
5
2
B = - 
558069
140
    (2)
- 
49
25
C = 
781473
625
    (3)
 D = - 
5384871
500
    (4)

Multiply both sides of equation (3) by 25
Divide both sides of equation (3) by 49, get the equation：
        -1C = 
111639
175
    (13)
, then add the two sides of equation (13) to both sides of equation (1), get the equation：
 A + B = 
809059
350
    (1)
- 
5
2
B = - 
558069
140
    (2)
- 
49
25
C = 
781473
625
    (3)
 D = - 
5384871
500
    (4)

Multiply both sides of equation (2) by 2
Divide both sides of equation (2) by 5, get the equation：
        -1B = - 
558069
350
    (14)
, then add the two sides of equation (14) to both sides of equation (1), get the equation：
 A = 
25099
35
    (1)
- 
5
2
B = - 
558069
140
    (2)
 C = - 
111639
175
    (3)
 D = - 
5384871
500
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
25099
35
    (1)
 B = 
558069
350
    (2)
 C = - 
111639
175
    (3)
 D = - 
5384871
500
    (4)


Therefore, the solution of the equation set is:
A = 
25099
35
B = 
558069
350
C = - 
111639
175
D = - 
5384871
500


Convert the solution of the equation set to decimals:
A = 717.114286
B = 1594.482857
C = -637.937143
D = -10769.742000

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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