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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:
-1A + D = 0    (1)
- 
31
25
E + F = 
3472
5
    (2)
 930D - 
682
5
E = 
527744
5
    (3)
-1B + C = 0    (4)
 E = 
12999
5
    (5)
-210B + 2250C = 
9217864
5
    (6)
Question solving process:

交After the exchange of equation (2) and equation (4)， the equation system becomes:
-1A + D = 0    (1)
-1B + C = 0    (2)
 930D - 
682
5
E = 
527744
5
    (3)
- 
31
25
E + F = 
3472
5
    (4)
 E = 
12999
5
    (5)
-210B + 2250C = 
9217864
5
    (6)

Multiply both sides of equation (2) by 210, the equation can be obtained:
        -210B + 210C = 0    (7)
, then subtract both sides of equation (7) from both sides of equation (6), the equations are reduced to:
-1A + D = 0    (1)
-1B + C = 0    (2)
 930D - 
682
5
E = 
527744
5
    (3)
- 
31
25
E + F = 
3472
5
    (4)
 E = 
12999
5
    (5)
 2040C = 
9217864
5
    (6)

交After the exchange of equation (3) and equation (6)， the equation system becomes:
-1A + D = 0    (1)
-1B + C = 0    (2)
 2040C = 
9217864
5
    (3)
- 
31
25
E + F = 
3472
5
    (4)
 E = 
12999
5
    (5)
 930D - 
682
5
E = 
527744
5
    (6)

交After the exchange of equation (4) and equation (6)， the equation system becomes:
-1A + D = 0    (1)
-1B + C = 0    (2)
 2040C = 
9217864
5
    (3)
 930D - 
682
5
E = 
527744
5
    (4)
 E = 
12999
5
    (5)
- 
31
25
E + F = 
3472
5
    (6)

Multiply both sides of equation (5) by 31
Divide the two sides of equation (5) by 25, the equation can be obtained:
         
31
25
E = 
402969
125
    (8)
, then add the two sides of equation (8) to both sides of equation (6), the equations are reduced to:
-1A + D = 0    (1)
-1B + C = 0    (2)
 2040C = 
9217864
5
    (3)
 930D - 
682
5
E = 
527744
5
    (4)
 E = 
12999
5
    (5)
 F = 
489769
125
    (6)

Multiply both sides of equation (5) by 682
Divide both sides of equation (5) by 5, get the equation：
         
682
5
E = 
8865318
25
    (9)
, then add the two sides of equation (9) to both sides of equation (4), get the equation：
-1A + D = 0    (1)
-1B + C = 0    (2)
 2040C = 
9217864
5
    (3)
 930D = 
11504038
25
    (4)
 E = 
12999
5
    (5)
 F = 
489769
125
    (6)

Divide both sides of equation (4) by 930, get the equation：
         D = 
185549
375
    (10)
, then subtract both sides of equation (10) from both sides of equation (1), get the equation：
-1A = - 
185549
375
    (1)
-1B + C = 0    (2)
 2040C = 
9217864
5
    (3)
 930D = 
11504038
25
    (4)
 E = 
12999
5
    (5)
 F = 
489769
125
    (6)

Divide both sides of equation (3) by 2040, get the equation：
         C = 
1152233
1275
    (11)
, then subtract both sides of equation (11) from both sides of equation (2), get the equation：
-1A = - 
185549
375
    (1)
-1B = - 
1152233
1275
    (2)
 2040C = 
9217864
5
    (3)
 D = 
185549
375
    (4)
 E = 
12999
5
    (5)
 F = 
489769
125
    (6)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
185549
375
    (1)
 B = 
1152233
1275
    (2)
 C = 
1152233
1275
    (3)
 D = 
185549
375
    (4)
 E = 
12999
5
    (5)
 F = 
489769
125
    (6)


Therefore, the solution of the equation set is:
A = 
185549
375
B = 
1152233
1275
C = 
1152233
1275
D = 
185549
375
E = 
12999
5
F = 
489769
125


Convert the solution of the equation set to decimals:
A = 494.797333
B = 903.712157
C = 903.712157
D = 494.797333
E = 2599.800000
F = 3918.152000

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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