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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)
 2A + 2B = 7000    (3)
 2A = 4120    (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)
 2A + 2B = 7000    (3)
 2A = 4120    (4)

Divide the two sides of equation (1) by 80, the equation can be obtained:
         2A + 
25
8
B + 
15
4
C + 
15
2
D = 
782127
20
    (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)
- 
9
8
B - 
15
4
C - 
15
2
D = - 
642127
20
    (3)
 2A = 4120    (4)

Divide the two sides of equation (1) by 80, the equation can be obtained:
         2A + 
25
8
B + 
15
4
C + 
15
2
D = 
782127
20
    (7)
, then subtract both sides of equation (7) 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)
- 
9
8
B - 
15
4
C - 
15
2
D = - 
642127
20
    (3)
- 
25
8
B - 
15
4
C - 
15
2
D = - 
699727
20
    (4)

Multiply both sides of equation (2) by 2, the equation can be obtained:
        - 
9
8
B - 
7
4
C - 
11
2
D = - 
297087
20
    (8)
, then subtract both sides of equation (8) 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)
-2C -2D = -17252    (3)
- 
25
8
B - 
15
4
C - 
15
2
D = - 
699727
20
    (4)

Multiply both sides of equation (2) by 50
Divide the two sides of equation (2) by 9, the equation can be obtained:
        - 
25
8
B - 
175
36
C - 
275
18
D = - 
495145
12
    (9)
, then subtract both sides of equation (9) 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)
-2C -2D = -17252    (3)
 
10
9
C + 
70
9
D = 
94136
15
    (4)

Multiply both sides of equation (3) by 5
Divide the two sides of equation (3) by 9, the equation can be obtained:
        - 
10
9
C - 
10
9
D = - 
86260
9
    (10)
, then add the two sides of equation (10) 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)
-2C -2D = -17252    (3)
 
20
3
D = - 
148892
45
    (4)

Multiply both sides of equation (4) by 3
Divide both sides of equation (4) by 10, get the equation：
         2D = - 
74446
75
    (11)
, then add the two sides of equation (11) 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)
-2C = - 
1368346
75
    (3)
 
20
3
D = - 
148892
45
    (4)

Multiply both sides of equation (4) by 33
Divide both sides of equation (4) by 80, get the equation：
         
11
4
D = - 
409453
300
    (12)
, then add the two sides of equation (12) to both sides of equation (2), get the equation：
 160A + 250B + 300C + 600D = 3128508    (1)
- 
9
16
B - 
7
8
C = - 
5275211
600
    (2)
-2C = - 
1368346
75
    (3)
 
20
3
D = - 
148892
45
    (4)

Multiply both sides of equation (4) by 90, get the equation：
         600D = -297784    (13)
, then subtract both sides of equation (13) from both sides of equation (1), get the equation：
 160A + 250B + 300C = 3426292    (1)
- 
9
16
B - 
7
8
C = - 
5275211
600
    (2)
-2C = - 
1368346
75
    (3)
 
20
3
D = - 
148892
45
    (4)

Multiply both sides of equation (3) by 7
Divide both sides of equation (3) by 16, get the equation：
        - 
7
8
C = - 
4789211
600
    (14)
, then subtract both sides of equation (14) from both sides of equation (2), get the equation：
 160A + 250B + 300C = 3426292    (1)
- 
9
16
B = -810    (2)
-2C = - 
1368346
75
    (3)
 D = - 
37223
75
    (4)

Multiply both sides of equation (3) by 150, get the equation：
        -300C = -2736692    (15)
, then add the two sides of equation (15) to both sides of equation (1), get the equation：
 160A + 250B = 689600    (1)
- 
9
16
B = -810    (2)
-2C = - 
1368346
75
    (3)
 D = - 
37223
75
    (4)

Multiply both sides of equation (2) by 4000
Divide both sides of equation (2) by 9, get the equation：
        -250B = -360000    (16)
, then add the two sides of equation (16) to both sides of equation (1), get the equation：
 160A = 329600    (1)
- 
9
16
B = -810    (2)
 C = 
684173
75
    (3)
 D = - 
37223
75
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 2060    (1)
 B = 1440    (2)
 C = 
684173
75
    (3)
 D = - 
37223
75
    (4)


Therefore, the solution of the equation set is:
A = 2060
B = 1440
C = 
684173
75
D = - 
37223
75


Convert the solution of the equation set to decimals:
A = 2060
B = 1440
C = 9122.306667
D = -496.306667

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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