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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 + 9B + 8C + 7D = 100    (1)
 9A + 8B + 7C + D = 200    (2)
 8A + 7B + C + 9D = 300    (3)
 7A + B + 9C + 8D = 400    (4)
Question solving process:

Multiply both sides of equation (1) by 9, the equation can be obtained:
         9A + 81B + 72C + 63D = 900    (5)
, then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
 A + 9B + 8C + 7D = 100    (1)
-73B -65C -62D = -700    (2)
 8A + 7B + C + 9D = 300    (3)
 7A + B + 9C + 8D = 400    (4)

Multiply both sides of equation (1) by 8, the equation can be obtained:
         8A + 72B + 64C + 56D = 800    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 A + 9B + 8C + 7D = 100    (1)
-73B -65C -62D = -700    (2)
-65B -63C -47D = -500    (3)
 7A + B + 9C + 8D = 400    (4)

Multiply both sides of equation (1) by 7, the equation can be obtained:
         7A + 63B + 56C + 49D = 700    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 A + 9B + 8C + 7D = 100    (1)
-73B -65C -62D = -700    (2)
-65B -63C -47D = -500    (3)
-62B -47C -41D = -300    (4)

Multiply both sides of equation (2) by 65
Divide the two sides of equation (2) by 73, the equation can be obtained:
        -65B - 
4225
73
C - 
4030
73
D = - 
45500
73
    (8)
, then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
 A + 9B + 8C + 7D = 100    (1)
-73B -65C -62D = -700    (2)
- 
374
73
C + 
599
73
D = 
9000
73
    (3)
-62B -47C -41D = -300    (4)

Multiply both sides of equation (2) by 62
Divide the two sides of equation (2) by 73, the equation can be obtained:
        -62B - 
4030
73
C - 
3844
73
D = - 
43400
73
    (9)
, then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
 A + 9B + 8C + 7D = 100    (1)
-73B -65C -62D = -700    (2)
- 
374
73
C + 
599
73
D = 
9000
73
    (3)
 
599
73
C + 
851
73
D = 
21500
73
    (4)

Multiply both sides of equation (3) by 599
Divide the two sides of equation (3) by 374, the equation can be obtained:
        - 
599
73
C + 
358801
27302
D = 
2695500
13651
    (10)
, then add the two sides of equation (10) to both sides of equation (4), the equations are reduced to:
 A + 9B + 8C + 7D = 100    (1)
-73B -65C -62D = -700    (2)
- 
374
73
C + 
599
73
D = 
9000
73
    (3)
 
9275
374
D = 
92000
187
    (4)

Multiply both sides of equation (4) by 224026
Divide both sides of equation (4) by 677075, get the equation：
         
599
73
D = 
4408640
27083
    (11)
, then subtract both sides of equation (11) from both sides of equation (3), get the equation：
 A + 9B + 8C + 7D = 100    (1)
-73B -65C -62D = -700    (2)
- 
374
73
C = - 
1069640
27083
    (3)
 
9275
374
D = 
92000
187
    (4)

Multiply both sides of equation (4) by 23188
Divide both sides of equation (4) by 9275, get the equation：
         62D = 
456320
371
    (12)
, then add the two sides of equation (12) to both sides of equation (2), get the equation：
 A + 9B + 8C + 7D = 100    (1)
-73B -65C = 
196620
371
    (2)
- 
374
73
C = - 
1069640
27083
    (3)
 
9275
374
D = 
92000
187
    (4)

Multiply both sides of equation (4) by 374
Divide both sides of equation (4) by 1325, get the equation：
         7D = 
7360
53
    (13)
, then subtract both sides of equation (13) from both sides of equation (1), get the equation：
 A + 9B + 8C = - 
2060
53
    (1)
-73B -65C = 
196620
371
    (2)
- 
374
73
C = - 
1069640
27083
    (3)
 
9275
374
D = 
92000
187
    (4)

Multiply both sides of equation (3) by 4745
Divide both sides of equation (3) by 374, get the equation：
        -65C = - 
185900
371
    (14)
, then subtract both sides of equation (14) from both sides of equation (2), get the equation：
 A + 9B + 8C = - 
2060
53
    (1)
-73B = 
382520
371
    (2)
- 
374
73
C = - 
1069640
27083
    (3)
 D = 
7360
371
    (4)

Multiply both sides of equation (3) by 292
Divide both sides of equation (3) by 187, get the equation：
        -8C = - 
22880
371
    (15)
, then add the two sides of equation (15) to both sides of equation (1), get the equation：
 A + 9B = - 
37300
371
    (1)
-73B = 
382520
371
    (2)
- 
374
73
C = - 
1069640
27083
    (3)
 D = 
7360
371
    (4)

Multiply both sides of equation (2) by 9
Divide both sides of equation (2) by 73, get the equation：
        -9B = 
47160
371
    (16)
, then add the two sides of equation (16) to both sides of equation (1), get the equation：
 A = 
9860
371
    (1)
-73B = 
382520
371
    (2)
 C = 
2860
371
    (3)
 D = 
7360
371
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
9860
371
    (1)
 B = - 
5240
371
    (2)
 C = 
2860
371
    (3)
 D = 
7360
371
    (4)


Therefore, the solution of the equation set is:
A = 
9860
371
B = - 
5240
371
C = 
2860
371
D = 
7360
371


Convert the solution of the equation set to decimals:
A = 26.576819
B = -14.123989
C = 7.708895
D = 19.838275

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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