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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)
 A + 2B = 5010    (3)
 C = 2100    (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)
 A + 2B = 5010    (3)
 C = 2100    (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 (3), the equations are reduced to:
 160A + 250B + 300C + 600D = 3128508    (1)
- 
9
16
B - 
7
8
C - 
11
4
D = - 
297087
40
    (2)
 
7
16
B - 
15
8
C - 
15
4
D = - 
581727
40
    (3)
 C = 2100    (4)

Multiply both sides of equation (2) by 7
Divide the two sides of equation (2) by 9, the equation can be obtained:
        - 
7
16
B - 
49
72
C - 
77
36
D = - 
693203
120
    (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)
- 
23
9
C - 
53
9
D = - 
304798
15
    (3)
 C = 2100    (4)

Multiply both sides of equation (3) by 9
Divide the two sides of equation (3) by 23, the equation can be obtained:
        -1C - 
53
23
D = - 
914394
115
    (8)
, then add the two sides of equation (8) 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)
- 
23
9
C - 
53
9
D = - 
304798
15
    (3)
- 
53
23
D = - 
672894
115
    (4)

Multiply both sides of equation (4) by 23
Divide both sides of equation (4) by 9, get the equation：
        - 
53
9
D = - 
74766
5
    (9)
, then subtract both sides of equation (9) from 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)
- 
23
9
C = - 
16100
3
    (3)
- 
53
23
D = - 
672894
115
    (4)

Multiply both sides of equation (4) by 253
Divide both sides of equation (4) by 212, get the equation：
        - 
11
4
D = - 
3700917
530
    (10)
, then subtract both sides of equation (10) from both sides of equation (2), get the equation：
 160A + 250B + 300C + 600D = 3128508    (1)
- 
9
16
B - 
7
8
C = - 
941943
2120
    (2)
- 
23
9
C = - 
16100
3
    (3)
- 
53
23
D = - 
672894
115
    (4)

Multiply both sides of equation (4) by 13800
Divide both sides of equation (4) by 53, get the equation：
        -600D = - 
80747280
53
    (11)
, then add the two sides of equation (11) to both sides of equation (1), get the equation：
 160A + 250B + 300C = 
85063644
53
    (1)
- 
9
16
B - 
7
8
C = - 
941943
2120
    (2)
- 
23
9
C = - 
16100
3
    (3)
- 
53
23
D = - 
672894
115
    (4)

Multiply both sides of equation (3) by 63
Divide both sides of equation (3) by 184, get the equation：
        - 
7
8
C = - 
3675
2
    (12)
, then subtract both sides of equation (12) from both sides of equation (2), get the equation：
 160A + 250B + 300C = 
85063644
53
    (1)
- 
9
16
B = 
2953557
2120
    (2)
- 
23
9
C = - 
16100
3
    (3)
 D = 
672894
265
    (4)

Multiply both sides of equation (3) by 2700
Divide both sides of equation (3) by 23, get the equation：
        -300C = -630000    (13)
, then add the two sides of equation (13) to both sides of equation (1), get the equation：
 160A + 250B = 
51673644
53
    (1)
- 
9
16
B = 
2953557
2120
    (2)
- 
23
9
C = - 
16100
3
    (3)
 D = 
672894
265
    (4)

Multiply both sides of equation (2) by 4000
Divide both sides of equation (2) by 9, get the equation：
        -250B = 
32817300
53
    (14)
, then add the two sides of equation (14) to both sides of equation (1), get the equation：
 160A = 
84490944
53
    (1)
- 
9
16
B = 
2953557
2120
    (2)
 C = 2100    (3)
 D = 
672894
265
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
2640342
265
    (1)
 B = - 
656346
265
    (2)
 C = 2100    (3)
 D = 
672894
265
    (4)


Therefore, the solution of the equation set is:
A = 
2640342
265
B = - 
656346
265
C = 2100
D = 
672894
265


Convert the solution of the equation set to decimals:
A = 9963.554717
B = -2476.777358
C = 2100
D = 2539.222642

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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