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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:
 5A + 3B + 3C + 3D = 2020    (1)
 3A + 3B + 3C + 5D = 2021    (2)
 3A + 3C + 8D = 2023    (3)
 3A + 6C + 5D = 2024    (4)
Question solving process:

Multiply both sides of equation (1) by 3
Divide the two sides of equation (1) by 5, the equation can be obtained:
         3A + 
9
5
B + 
9
5
C + 
9
5
D = 1212    (5)
, then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
 5A + 3B + 3C + 3D = 2020    (1)
 
6
5
B + 
6
5
C + 
16
5
D = 809    (2)
 3A + 3C + 8D = 2023    (3)
 3A + 6C + 5D = 2024    (4)

Multiply both sides of equation (1) by 3
Divide the two sides of equation (1) by 5, the equation can be obtained:
         3A + 
9
5
B + 
9
5
C + 
9
5
D = 1212    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 5A + 3B + 3C + 3D = 2020    (1)
 
6
5
B + 
6
5
C + 
16
5
D = 809    (2)
- 
9
5
B + 
6
5
C + 
31
5
D = 811    (3)
 3A + 6C + 5D = 2024    (4)

Multiply both sides of equation (1) by 3
Divide the two sides of equation (1) by 5, the equation can be obtained:
         3A + 
9
5
B + 
9
5
C + 
9
5
D = 1212    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 5A + 3B + 3C + 3D = 2020    (1)
 
6
5
B + 
6
5
C + 
16
5
D = 809    (2)
- 
9
5
B + 
6
5
C + 
31
5
D = 811    (3)
- 
9
5
B + 
21
5
C + 
16
5
D = 812    (4)

Multiply both sides of equation (2) by 3
Divide the two sides of equation (2) by 2, the equation can be obtained:
         
9
5
B + 
9
5
C + 
24
5
D = 
2427
2
    (8)
, then add the two sides of equation (8) to both sides of equation (3), the equations are reduced to:
 5A + 3B + 3C + 3D = 2020    (1)
 
6
5
B + 
6
5
C + 
16
5
D = 809    (2)
 3C + 11D = 
4049
2
    (3)
- 
9
5
B + 
21
5
C + 
16
5
D = 812    (4)

Multiply both sides of equation (2) by 3
Divide the two sides of equation (2) by 2, the equation can be obtained:
         
9
5
B + 
9
5
C + 
24
5
D = 
2427
2
    (9)
, then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
 5A + 3B + 3C + 3D = 2020    (1)
 
6
5
B + 
6
5
C + 
16
5
D = 809    (2)
 3C + 11D = 
4049
2
    (3)
 6C + 8D = 
4051
2
    (4)

Multiply both sides of equation (3) by 2, the equation can be obtained:
         6C + 22D = 4049    (10)
, then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
 5A + 3B + 3C + 3D = 2020    (1)
 
6
5
B + 
6
5
C + 
16
5
D = 809    (2)
 3C + 11D = 
4049
2
    (3)
-14D = - 
4047
2
    (4)

Multiply both sides of equation (4) by 11
Divide both sides of equation (4) by 14, get the equation：
        -11D = - 
44517
28
    (11)
, then add the two sides of equation (11) to both sides of equation (3), get the equation：
 5A + 3B + 3C + 3D = 2020    (1)
 
6
5
B + 
6
5
C + 
16
5
D = 809    (2)
 3C = 
12169
28
    (3)
-14D = - 
4047
2
    (4)

Multiply both sides of equation (4) by 8
Divide both sides of equation (4) by 35, get the equation：
        - 
16
5
D = - 
16188
35
    (12)
, then add the two sides of equation (12) to both sides of equation (2), get the equation：
 5A + 3B + 3C + 3D = 2020    (1)
 
6
5
B + 
6
5
C = 
12127
35
    (2)
 3C = 
12169
28
    (3)
-14D = - 
4047
2
    (4)

Multiply both sides of equation (4) by 3
Divide both sides of equation (4) by 14, get the equation：
        -3D = - 
12141
28
    (13)
, then add the two sides of equation (13) to both sides of equation (1), get the equation：
 5A + 3B + 3C = 
44419
28
    (1)
 
6
5
B + 
6
5
C = 
12127
35
    (2)
 3C = 
12169
28
    (3)
-14D = - 
4047
2
    (4)

Multiply both sides of equation (3) by 2
Divide both sides of equation (3) by 5, get the equation：
         
6
5
C = 
12169
70
    (14)
, then subtract both sides of equation (14) from both sides of equation (2), get the equation：
 5A + 3B + 3C = 
44419
28
    (1)
 
6
5
B = 
2417
14
    (2)
 3C = 
12169
28
    (3)
 D = 
4047
28
    (4)

Subtract both sides of equation (3) from both sides of equation (1), get the equation：
 5A + 3B = 
16125
14
    (1)
 
6
5
B = 
2417
14
    (2)
 3C = 
12169
28
    (3)
 D = 
4047
28
    (4)

Multiply both sides of equation (2) by 5
Divide both sides of equation (2) by 2, get the equation：
         3B = 
12085
28
    (15)
, then subtract both sides of equation (15) from both sides of equation (1), get the equation：
 5A = 
20165
28
    (1)
 
6
5
B = 
2417
14
    (2)
 C = 
12169
84
    (3)
 D = 
4047
28
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
4033
28
    (1)
 B = 
12085
84
    (2)
 C = 
12169
84
    (3)
 D = 
4047
28
    (4)


Therefore, the solution of the equation set is:
A = 
4033
28
B = 
12085
84
C = 
12169
84
D = 
4047
28


Convert the solution of the equation set to decimals:
A = 144.035714
B = 143.869048
C = 144.869048
D = 144.535714

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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