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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 + 3B + 2C + 5D = 3    (1)
-5A + 5B + 7C + 4D = 11    (2)
 3A + B + 8C + 5D = 5    (3)
 9A + 2B + C + D = 6    (4)
Question solving process:

Multiply both sides of equation (1) by 5, the equation can be obtained:
         5A + 15B + 10C + 25D = 15    (5)
, then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
 A + 3B + 2C + 5D = 3    (1)
 20B + 17C + 29D = 26    (2)
 3A + B + 8C + 5D = 5    (3)
 9A + 2B + C + D = 6    (4)

Multiply both sides of equation (1) by 3, the equation can be obtained:
         3A + 9B + 6C + 15D = 9    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 A + 3B + 2C + 5D = 3    (1)
 20B + 17C + 29D = 26    (2)
-8B + 2C -10D = -4    (3)
 9A + 2B + C + D = 6    (4)

Multiply both sides of equation (1) by 9, the equation can be obtained:
         9A + 27B + 18C + 45D = 27    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 A + 3B + 2C + 5D = 3    (1)
 20B + 17C + 29D = 26    (2)
-8B + 2C -10D = -4    (3)
-25B -17C -44D = -21    (4)

Multiply both sides of equation (2) by 2
Divide the two sides of equation (2) by 5, the equation can be obtained:
         8B + 
34
5
C + 
58
5
D = 
52
5
    (8)
, then add the two sides of equation (8) to both sides of equation (3), the equations are reduced to:
 A + 3B + 2C + 5D = 3    (1)
 20B + 17C + 29D = 26    (2)
 
44
5
C + 
8
5
D = 
32
5
    (3)
-25B -17C -44D = -21    (4)

Multiply both sides of equation (2) by 5
Divide the two sides of equation (2) by 4, the equation can be obtained:
         25B + 
85
4
C + 
145
4
D = 
65
2
    (9)
, then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
 A + 3B + 2C + 5D = 3    (1)
 20B + 17C + 29D = 26    (2)
 
44
5
C + 
8
5
D = 
32
5
    (3)
 
17
4
C - 
31
4
D = 
23
2
    (4)

Multiply both sides of equation (3) by 85
Divide the two sides of equation (3) by 176, the equation can be obtained:
         
17
4
C + 
17
22
D = 
34
11
    (10)
, then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
 A + 3B + 2C + 5D = 3    (1)
 20B + 17C + 29D = 26    (2)
 
44
5
C + 
8
5
D = 
32
5
    (3)
- 
375
44
D = 
185
22
    (4)

Multiply both sides of equation (4) by 352
Divide both sides of equation (4) by 1875, get the equation：
        - 
8
5
D = 
592
375
    (11)
, then add the two sides of equation (11) to both sides of equation (3), get the equation：
 A + 3B + 2C + 5D = 3    (1)
 20B + 17C + 29D = 26    (2)
 
44
5
C = 
2992
375
    (3)
- 
375
44
D = 
185
22
    (4)

Multiply both sides of equation (4) by 1276
Divide both sides of equation (4) by 375, get the equation：
        -29D = 
2146
75
    (12)
, then add the two sides of equation (12) to both sides of equation (2), get the equation：
 A + 3B + 2C + 5D = 3    (1)
 20B + 17C = 
4096
75
    (2)
 
44
5
C = 
2992
375
    (3)
- 
375
44
D = 
185
22
    (4)

Multiply both sides of equation (4) by 44
Divide both sides of equation (4) by 75, get the equation：
        -5D = 
74
15
    (13)
, then add the two sides of equation (13) to both sides of equation (1), get the equation：
 A + 3B + 2C = 
119
15
    (1)
 20B + 17C = 
4096
75
    (2)
 
44
5
C = 
2992
375
    (3)
- 
375
44
D = 
185
22
    (4)

Multiply both sides of equation (3) by 85
Divide both sides of equation (3) by 44, get the equation：
         17C = 
1156
75
    (14)
, then subtract both sides of equation (14) from both sides of equation (2), get the equation：
 A + 3B + 2C = 
119
15
    (1)
 20B = 
196
5
    (2)
 
44
5
C = 
2992
375
    (3)
 D = - 
74
75
    (4)

Multiply both sides of equation (3) by 5
Divide both sides of equation (3) by 22, get the equation：
         2C = 
136
75
    (15)
, then subtract both sides of equation (15) from both sides of equation (1), get the equation：
 A + 3B = 
153
25
    (1)
 20B = 
196
5
    (2)
 
44
5
C = 
2992
375
    (3)
 D = - 
74
75
    (4)

Multiply both sides of equation (2) by 3
Divide both sides of equation (2) by 20, get the equation：
         3B = 
147
25
    (16)
, then subtract both sides of equation (16) from both sides of equation (1), get the equation：
 A = 
6
25
    (1)
 20B = 
196
5
    (2)
 C = 
68
75
    (3)
 D = - 
74
75
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
6
25
    (1)
 B = 
49
25
    (2)
 C = 
68
75
    (3)
 D = - 
74
75
    (4)


Therefore, the solution of the equation set is:
A = 
6
25
B = 
49
25
C = 
68
75
D = - 
74
75


Convert the solution of the equation set to decimals:
A = 0.240000
B = 1.960000
C = 0.906667
D = -0.986667

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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