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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:
 10B + 8D + 2F = 40    (1)
 10A + 10B + 4C = -20    (2)
 4C + 8D + 8E = 20    (3)
 A -1B + F = 0    (4)
-1B + C + D = 0    (5)
-1A + C + E = 0    (6)
Question solving process:

交After the exchange of equation (1) and equation (2)， the equation system becomes:
 10A + 10B + 4C = -20    (1)
 10B + 8D + 2F = 40    (2)
 4C + 8D + 8E = 20    (3)
 A -1B + F = 0    (4)
-1B + C + D = 0    (5)
-1A + C + E = 0    (6)

Divide the two sides of equation (1) by 10, the equation can be obtained:
         A + B + 
2
5
C = -2    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 10A + 10B + 4C = -20    (1)
 10B + 8D + 2F = 40    (2)
 4C + 8D + 8E = 20    (3)
-2B - 
2
5
C + F = 2    (4)
-1B + C + D = 0    (5)
-1A + C + E = 0    (6)

Divide the two sides of equation (1) by 10, the equation can be obtained:
         A + B + 
2
5
C = -2    (8)
, then add the two sides of equation (8) to both sides of equation (6), the equations are reduced to:
 10A + 10B + 4C = -20    (1)
 10B + 8D + 2F = 40    (2)
 4C + 8D + 8E = 20    (3)
-2B - 
2
5
C + F = 2    (4)
-1B + C + D = 0    (5)
 B + 
7
5
C + E = -2    (6)

Divide the two sides of equation (2) by 5, the equation can be obtained:
         2B + 
8
5
D + 
2
5
F = 8    (9)
, then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
 10A + 10B + 4C = -20    (1)
 10B + 8D + 2F = 40    (2)
 4C + 8D + 8E = 20    (3)
- 
2
5
C + 
8
5
D + 
7
5
F = 10    (4)
-1B + C + D = 0    (5)
 B + 
7
5
C + E = -2    (6)

Divide the two sides of equation (2) by 10, the equation can be obtained:
         B + 
4
5
D + 
1
5
F = 4    (10)
, then add the two sides of equation (10) to both sides of equation (5), the equations are reduced to:
 10A + 10B + 4C = -20    (1)
 10B + 8D + 2F = 40    (2)
 4C + 8D + 8E = 20    (3)
- 
2
5
C + 
8
5
D + 
7
5
F = 10    (4)
 C + 
9
5
D + 
1
5
F = 4    (5)
 B + 
7
5
C + E = -2    (6)

Divide the two sides of equation (2) by 10, the equation can be obtained:
         B + 
4
5
D + 
1
5
F = 4    (11)
, then subtract both sides of equation (11) from both sides of equation (6), the equations are reduced to:
 10A + 10B + 4C = -20    (1)
 10B + 8D + 2F = 40    (2)
 4C + 8D + 8E = 20    (3)
- 
2
5
C + 
8
5
D + 
7
5
F = 10    (4)
 C + 
9
5
D + 
1
5
F = 4    (5)
 
7
5
C - 
4
5
D + E - 
1
5
F = -6    (6)

Divide the two sides of equation (3) by 10, the equation can be obtained:
         
2
5
C + 
4
5
D + 
4
5
E = 2    (12)
, then add the two sides of equation (12) to both sides of equation (4), the equations are reduced to:
 10A + 10B + 4C = -20    (1)
 10B + 8D + 2F = 40    (2)
 4C + 8D + 8E = 20    (3)
 
12
5
D + 
4
5
E + 
7
5
F = 12    (4)
 C + 
9
5
D + 
1
5
F = 4    (5)
 
7
5
C - 
4
5
D + E - 
1
5
F = -6    (6)

Divide the two sides of equation (3) by 4, the equation can be obtained:
         C + 2D + 2E = 5    (13)
, then subtract both sides of equation (13) from both sides of equation (5), the equations are reduced to:
 10A + 10B + 4C = -20    (1)
 10B + 8D + 2F = 40    (2)
 4C + 8D + 8E = 20    (3)
 
12
5
D + 
4
5
E + 
7
5
F = 12    (4)
- 
1
5
D -2E + 
1
5
F = -1    (5)
 
7
5
C - 
4
5
D + E - 
1
5
F = -6    (6)

Multiply both sides of equation (3) by 7
Divide the two sides of equation (3) by 20, the equation can be obtained:
         
7
5
C + 
14
5
D + 
14
5
E = 7    (14)
, then subtract both sides of equation (14) from both sides of equation (6), the equations are reduced to:
 10A + 10B + 4C = -20    (1)
 10B + 8D + 2F = 40    (2)
 4C + 8D + 8E = 20    (3)
 
12
5
D + 
4
5
E + 
7
5
F = 12    (4)
- 
1
5
D -2E + 
1
5
F = -1    (5)
- 
18
5
D - 
9
5
E - 
1
5
F = -13    (6)

Divide the two sides of equation (4) by 12, the equation can be obtained:
         
1
5
D + 
1
15
E + 
7
60
F = 1    (15)
, then add the two sides of equation (15) to both sides of equation (5), the equations are reduced to:
 10A + 10B + 4C = -20    (1)
 10B + 8D + 2F = 40    (2)
 4C + 8D + 8E = 20    (3)
 
12
5
D + 
4
5
E + 
7
5
F = 12    (4)
- 
29
15
E + 
19
60
F = 0    (5)
- 
18
5
D - 
9
5
E - 
1
5
F = -13    (6)

Multiply both sides of equation (4) by 3
Divide the two sides of equation (4) by 2, the equation can be obtained:
         
18
5
D + 
6
5
E + 
21
10
F = 18    (16)
, then add the two sides of equation (16) to both sides of equation (6), the equations are reduced to:
 10A + 10B + 4C = -20    (1)
 10B + 8D + 2F = 40    (2)
 4C + 8D + 8E = 20    (3)
 
12
5
D + 
4
5
E + 
7
5
F = 12    (4)
- 
29
15
E + 
19
60
F = 0    (5)
- 
3
5
E + 
19
10
F = 5    (6)

Multiply both sides of equation (5) by 9
Divide the two sides of equation (5) by 29, the equation can be obtained:
        - 
3
5
E + 
57
580
F = 0    (17)
, then subtract both sides of equation (17) from both sides of equation (6), the equations are reduced to:
 10A + 10B + 4C = -20    (1)
 10B + 8D + 2F = 40    (2)
 4C + 8D + 8E = 20    (3)
 
12
5
D + 
4
5
E + 
7
5
F = 12    (4)
- 
29
15
E + 
19
60
F = 0    (5)
 
209
116
F = 5    (6)

Multiply both sides of equation (6) by 29
Divide both sides of equation (6) by 165, get the equation：
         
19
60
F = 
29
33
    (18)
, then subtract both sides of equation (18) from both sides of equation (5), get the equation：
 10A + 10B + 4C = -20    (1)
 10B + 8D + 2F = 40    (2)
 4C + 8D + 8E = 20    (3)
 
12
5
D + 
4
5
E + 
7
5
F = 12    (4)
- 
29
15
E = - 
29
33
    (5)
 
209
116
F = 5    (6)

Multiply both sides of equation (6) by 812
Divide both sides of equation (6) by 1045, get the equation：
         
7
5
F = 
812
209
    (19)
, then subtract both sides of equation (19) from both sides of equation (4), get the equation：
 10A + 10B + 4C = -20    (1)
 10B + 8D + 2F = 40    (2)
 4C + 8D + 8E = 20    (3)
 
12
5
D + 
4
5
E = 
1696
209
    (4)
- 
29
15
E = - 
29
33
    (5)
 
209
116
F = 5    (6)

Multiply both sides of equation (6) by 232
Divide both sides of equation (6) by 209, get the equation：
         2F = 
1160
209
    (20)
, then subtract both sides of equation (20) from both sides of equation (2), get the equation：
 10A + 10B + 4C = -20    (1)
 10B + 8D = 
7200
209
    (2)
 4C + 8D + 8E = 20    (3)
 
12
5
D + 
4
5
E = 
1696
209
    (4)
- 
29
15
E = - 
29
33
    (5)
 
209
116
F = 5    (6)

Multiply both sides of equation (5) by 12
Divide both sides of equation (5) by 29, get the equation：
        - 
4
5
E = - 
4
11
    (21)
, then add the two sides of equation (21) to both sides of equation (4), get the equation：
 10A + 10B + 4C = -20    (1)
 10B + 8D = 
7200
209
    (2)
 4C + 8D + 8E = 20    (3)
 
12
5
D = 
1620
209
    (4)
- 
29
15
E = - 
29
33
    (5)
 F = 
580
209
    (6)

Multiply both sides of equation (5) by 120
Divide both sides of equation (5) by 29, get the equation：
        -8E = - 
40
11
    (22)
, then add the two sides of equation (22) to both sides of equation (3), get the equation：
 10A + 10B + 4C = -20    (1)
 10B + 8D = 
7200
209
    (2)
 4C + 8D = 
180
11
    (3)
 
12
5
D = 
1620
209
    (4)
- 
29
15
E = - 
29
33
    (5)
 F = 
580
209
    (6)

Multiply both sides of equation (4) by 10
Divide both sides of equation (4) by 3, get the equation：
         8D = 
5400
209
    (23)
, then subtract both sides of equation (23) from both sides of equation (3), get the equation：
 10A + 10B + 4C = -20    (1)
 10B + 8D = 
7200
209
    (2)
 4C = - 
180
19
    (3)
 
12
5
D = 
1620
209
    (4)
 E = 
5
11
    (5)
 F = 
580
209
    (6)

Multiply both sides of equation (4) by 10
Divide both sides of equation (4) by 3, get the equation：
         8D = 
5400
209
    (24)
, then subtract both sides of equation (24) from both sides of equation (2), get the equation：
 10A + 10B + 4C = -20    (1)
 10B = 
1800
209
    (2)
 4C = - 
180
19
    (3)
 
12
5
D = 
1620
209
    (4)
 E = 
5
11
    (5)
 F = 
580
209
    (6)

Subtract both sides of equation (3) from both sides of equation (1), get the equation：
 10A + 10B = - 
200
19
    (1)
 10B = 
1800
209
    (2)
 4C = - 
180
19
    (3)
 D = 
675
209
    (4)
 E = 
5
11
    (5)
 F = 
580
209
    (6)

Subtract both sides of equation (2) from both sides of equation (1), get the equation：
 10A = - 
4000
209
    (1)
 10B = 
1800
209
    (2)
 C = - 
45
19
    (3)
 D = 
675
209
    (4)
 E = 
5
11
    (5)
 F = 
580
209
    (6)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = - 
400
209
    (1)
 B = 
180
209
    (2)
 C = - 
45
19
    (3)
 D = 
675
209
    (4)
 E = 
5
11
    (5)
 F = 
580
209
    (6)


Therefore, the solution of the equation set is:
A = - 
400
209
B = 
180
209
C = - 
45
19
D = 
675
209
E = 
5
11
F = 
580
209


Convert the solution of the equation set to decimals:
A = -1.913876
B = 0.861244
C = -2.368421
D = 3.229665
E = 0.454545
F = 2.775120

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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