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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:
 160A + 250B + 300C + 600D = 3128508    (1)
 A + B + C + D = 12126    (2)
 B = 3851    (3)
 A = 5283    (4)
Question solving process:

Divide the two sides of equation (1) by 160, the equation can be obtained:
         A + 
25
16
B + 
15
8
C + 
15
4
D = 
782127
40
    (5)
, then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
 160A + 250B + 300C + 600D = 3128508    (1)
- 
9
16
B - 
7
8
C - 
11
4
D = - 
297087
40
    (2)
 B = 3851    (3)
 A = 5283    (4)

Divide the two sides of equation (1) by 160, the equation can be obtained:
         A + 
25
16
B + 
15
8
C + 
15
4
D = 
782127
40
    (6)
, then subtract both sides of equation (6) from both sides of equation (4), the equations are reduced to:
 160A + 250B + 300C + 600D = 3128508    (1)
- 
9
16
B - 
7
8
C - 
11
4
D = - 
297087
40
    (2)
 B = 3851    (3)
- 
25
16
B - 
15
8
C - 
15
4
D = - 
570807
40
    (4)

Multiply both sides of equation (2) by 16
Divide the two sides of equation (2) by 9, the equation can be obtained:
        -1B - 
14
9
C - 
44
9
D = - 
198058
15
    (7)
, then add the two sides of equation (7) to both sides of equation (3), the equations are reduced to:
 160A + 250B + 300C + 600D = 3128508    (1)
- 
9
16
B - 
7
8
C - 
11
4
D = - 
297087
40
    (2)
- 
14
9
C - 
44
9
D = - 
140293
15
    (3)
- 
25
16
B - 
15
8
C - 
15
4
D = - 
570807
40
    (4)

Multiply both sides of equation (2) by 25
Divide the two sides of equation (2) by 9, the equation can be obtained:
        - 
25
16
B - 
175
72
C - 
275
36
D = - 
495145
24
    (8)
, then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
 160A + 250B + 300C + 600D = 3128508    (1)
- 
9
16
B - 
7
8
C - 
11
4
D = - 
297087
40
    (2)
- 
14
9
C - 
44
9
D = - 
140293
15
    (3)
 
5
9
C + 
35
9
D = 
95413
15
    (4)

Multiply both sides of equation (3) by 5
Divide the two sides of equation (3) by 14, the equation can be obtained:
        - 
5
9
C - 
110
63
D = - 
140293
42
    (9)
, then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
 160A + 250B + 300C + 600D = 3128508    (1)
- 
9
16
B - 
7
8
C - 
11
4
D = - 
297087
40
    (2)
- 
14
9
C - 
44
9
D = - 
140293
15
    (3)
 
15
7
D = 
211439
70
    (4)

Multiply both sides of equation (4) by 308
Divide both sides of equation (4) by 135, get the equation：
         
44
9
D = 
4651658
675
    (10)
, then add the two sides of equation (10) to both sides of equation (3), get the equation：
 160A + 250B + 300C + 600D = 3128508    (1)
- 
9
16
B - 
7
8
C - 
11
4
D = - 
297087
40
    (2)
- 
14
9
C = - 
1661527
675
    (3)
 
15
7
D = 
211439
70
    (4)

Multiply both sides of equation (4) by 77
Divide both sides of equation (4) by 60, get the equation：
         
11
4
D = 
2325829
600
    (11)
, then add the two sides of equation (11) to both sides of equation (2), get the equation：
 160A + 250B + 300C + 600D = 3128508    (1)
- 
9
16
B - 
7
8
C = - 
532619
150
    (2)
- 
14
9
C = - 
1661527
675
    (3)
 
15
7
D = 
211439
70
    (4)

Multiply both sides of equation (4) by 280, get the equation：
         600D = 845756    (12)
, then subtract both sides of equation (12) from both sides of equation (1), get the equation：
 160A + 250B + 300C = 2282752    (1)
- 
9
16
B - 
7
8
C = - 
532619
150
    (2)
- 
14
9
C = - 
1661527
675
    (3)
 
15
7
D = 
211439
70
    (4)

Multiply both sides of equation (3) by 9
Divide both sides of equation (3) by 16, get the equation：
        - 
7
8
C = - 
1661527
1200
    (13)
, then subtract both sides of equation (13) from both sides of equation (2), get the equation：
 160A + 250B + 300C = 2282752    (1)
- 
9
16
B = - 
34659
16
    (2)
- 
14
9
C = - 
1661527
675
    (3)
 D = 
211439
150
    (4)

Multiply both sides of equation (3) by 1350
Divide both sides of equation (3) by 7, get the equation：
        -300C = -474722    (14)
, then add the two sides of equation (14) to both sides of equation (1), get the equation：
 160A + 250B = 1808030    (1)
- 
9
16
B = - 
34659
16
    (2)
- 
14
9
C = - 
1661527
675
    (3)
 D = 
211439
150
    (4)

Multiply both sides of equation (2) by 4000
Divide both sides of equation (2) by 9, get the equation：
        -250B = -962750    (15)
, then add the two sides of equation (15) to both sides of equation (1), get the equation：
 160A = 845280    (1)
- 
9
16
B = - 
34659
16
    (2)
 C = 
237361
150
    (3)
 D = 
211439
150
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 5283    (1)
 B = 3851    (2)
 C = 
237361
150
    (3)
 D = 
211439
150
    (4)


Therefore, the solution of the equation set is:
A = 5283
B = 3851
C = 
237361
150
D = 
211439
150


Convert the solution of the equation set to decimals:
A = 5283
B = 3851
C = 1582.406667
D = 1409.593333

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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