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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:
 B -1E + F = 0    (1)
 C -1D -1F = 0    (2)
-1A + D + E = 0    (3)
 
33
10
B - 
11
5
C -6F = -30    (4)
 3A + 
11
5
C + 6D = 44    (5)
-6D + 8E + 6F = 0    (6)
Question solving process:

交After the exchange of equation (1) and equation (3)， the equation system becomes:
-1A + D + E = 0    (1)
 C -1D -1F = 0    (2)
 B -1E + F = 0    (3)
 
33
10
B - 
11
5
C -6F = -30    (4)
 3A + 
11
5
C + 6D = 44    (5)
-6D + 8E + 6F = 0    (6)

Multiply both sides of equation (1) by 3, the equation can be obtained:
        -3A + 3D + 3E = 0    (7)
, then add the two sides of equation (7) to both sides of equation (5), the equations are reduced to:
-1A + D + E = 0    (1)
 C -1D -1F = 0    (2)
 B -1E + F = 0    (3)
 
33
10
B - 
11
5
C -6F = -30    (4)
 
11
5
C + 9D + 3E = 44    (5)
-6D + 8E + 6F = 0    (6)

交After the exchange of equation (2) and equation (3)， the equation system becomes:
-1A + D + E = 0    (1)
 B -1E + F = 0    (2)
 C -1D -1F = 0    (3)
 
33
10
B - 
11
5
C -6F = -30    (4)
 
11
5
C + 9D + 3E = 44    (5)
-6D + 8E + 6F = 0    (6)

Multiply both sides of equation (2) by 33
Divide the two sides of equation (2) by 10, the equation can be obtained:
         
33
10
B - 
33
10
E + 
33
10
F = 0    (8)
, then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
-1A + D + E = 0    (1)
 B -1E + F = 0    (2)
 C -1D -1F = 0    (3)
- 
11
5
C + 
33
10
E - 
93
10
F = -30    (4)
 
11
5
C + 9D + 3E = 44    (5)
-6D + 8E + 6F = 0    (6)

Multiply both sides of equation (3) by 11
Divide the two sides of equation (3) by 5, the equation can be obtained:
         
11
5
C - 
11
5
D - 
11
5
F = 0    (9)
, then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
-1A + D + E = 0    (1)
 B -1E + F = 0    (2)
 C -1D -1F = 0    (3)
- 
11
5
D + 
33
10
E - 
23
2
F = -30    (4)
 
11
5
C + 9D + 3E = 44    (5)
-6D + 8E + 6F = 0    (6)

Multiply both sides of equation (3) by 11
Divide the two sides of equation (3) by 5, the equation can be obtained:
         
11
5
C - 
11
5
D - 
11
5
F = 0    (10)
, then subtract both sides of equation (10) from both sides of equation (5), the equations are reduced to:
-1A + D + E = 0    (1)
 B -1E + F = 0    (2)
 C -1D -1F = 0    (3)
- 
11
5
D + 
33
10
E - 
23
2
F = -30    (4)
 
56
5
D + 3E + 
11
5
F = 44    (5)
-6D + 8E + 6F = 0    (6)

Multiply both sides of equation (4) by 56
Divide the two sides of equation (4) by 11, the equation can be obtained:
        - 
56
5
D + 
84
5
E - 
644
11
F = - 
1680
11
    (11)
, then add the two sides of equation (11) to both sides of equation (5), the equations are reduced to:
-1A + D + E = 0    (1)
 B -1E + F = 0    (2)
 C -1D -1F = 0    (3)
- 
11
5
D + 
33
10
E - 
23
2
F = -30    (4)
 
99
5
E - 
3099
55
F = - 
1196
11
    (5)
-6D + 8E + 6F = 0    (6)

Multiply both sides of equation (4) by 30
Divide the two sides of equation (4) by 11, the equation can be obtained:
        -6D + 9E - 
345
11
F = - 
900
11
    (12)
, then subtract both sides of equation (12) from both sides of equation (6), the equations are reduced to:
-1A + D + E = 0    (1)
 B -1E + F = 0    (2)
 C -1D -1F = 0    (3)
- 
11
5
D + 
33
10
E - 
23
2
F = -30    (4)
 
99
5
E - 
3099
55
F = - 
1196
11
    (5)
-1E + 
411
11
F = 
900
11
    (6)

Multiply both sides of equation (5) by 5
Divide the two sides of equation (5) by 99, the equation can be obtained:
         E - 
1033
363
F = - 
5980
1089
    (13)
, then add the two sides of equation (13) to both sides of equation (6), the equations are reduced to:
-1A + D + E = 0    (1)
 B -1E + F = 0    (2)
 C -1D -1F = 0    (3)
- 
11
5
D + 
33
10
E - 
23
2
F = -30    (4)
 
99
5
E - 
3099
55
F = - 
1196
11
    (5)
 
12530
363
F = 
83120
1089
    (6)

Multiply both sides of equation (6) by 102267
Divide both sides of equation (6) by 62650, get the equation：
         
554721
9845
F = 
8586296
68915
    (14)
, then add the two sides of equation (14) to both sides of equation (5), get the equation：
-1A + D + E = 0    (1)
 B -1E + F = 0    (2)
 C -1D -1F = 0    (3)
- 
11
5
D + 
33
10
E - 
23
2
F = -30    (4)
 
99
5
E = 
99396
6265
    (5)
 
12530
363
F = 
83120
1089
    (6)

Multiply both sides of equation (6) by 8349
Divide both sides of equation (6) by 25060, get the equation：
         
4117
358
F = 
95588
3759
    (15)
, then add the two sides of equation (15) to both sides of equation (4), get the equation：
-1A + D + E = 0    (1)
 B -1E + F = 0    (2)
 C -1D -1F = 0    (3)
- 
11
5
D + 
33
10
E = - 
17182
3759
    (4)
 
99
5
E = 
99396
6265
    (5)
 
12530
363
F = 
83120
1089
    (6)

Multiply both sides of equation (6) by 363
Divide both sides of equation (6) by 12530, get the equation：
         F = 
8312
3759
    (16)
, then add the two sides of equation (16) to both sides of equation (3), get the equation：
-1A + D + E = 0    (1)
 B -1E + F = 0    (2)
 C -1D = 
8312
3759
    (3)
- 
11
5
D + 
33
10
E = - 
17182
3759
    (4)
 
99
5
E = 
99396
6265
    (5)
 
12530
363
F = 
83120
1089
    (6)

Multiply both sides of equation (6) by 363
Divide both sides of equation (6) by 12530, get the equation：
         F = 
8312
3759
    (17)
, then subtract both sides of equation (17) from both sides of equation (2), get the equation：
-1A + D + E = 0    (1)
 B -1E = - 
8312
3759
    (2)
 C -1D = 
8312
3759
    (3)
- 
11
5
D + 
33
10
E = - 
17182
3759
    (4)
 
99
5
E = 
99396
6265
    (5)
 
12530
363
F = 
83120
1089
    (6)

Divide both sides of equation (5) by 6, get the equation：
         
33
10
E = 
16566
6265
    (18)
, then subtract both sides of equation (18) from both sides of equation (4), get the equation：
-1A + D + E = 0    (1)
 B -1E = - 
8312
3759
    (2)
 C -1D = 
8312
3759
    (3)
- 
11
5
D = - 
135608
18795
    (4)
 
99
5
E = 
99396
6265
    (5)
 F = 
8312
3759
    (6)

Multiply both sides of equation (5) by 5
Divide both sides of equation (5) by 99, get the equation：
         E = 
1004
1253
    (19)
, then add the two sides of equation (19) to both sides of equation (2), get the equation：
-1A + D + E = 0    (1)
 B = - 
5300
3759
    (2)
 C -1D = 
8312
3759
    (3)
- 
11
5
D = - 
135608
18795
    (4)
 
99
5
E = 
99396
6265
    (5)
 F = 
8312
3759
    (6)

Multiply both sides of equation (5) by 5
Divide both sides of equation (5) by 99, get the equation：
         E = 
1004
1253
    (20)
, then subtract both sides of equation (20) from both sides of equation (1), get the equation：
-1A + D = - 
1004
1253
    (1)
 B = - 
5300
3759
    (2)
 C -1D = 
8312
3759
    (3)
- 
11
5
D = - 
135608
18795
    (4)
 
99
5
E = 
99396
6265
    (5)
 F = 
8312
3759
    (6)

Multiply both sides of equation (4) by 5
Divide both sides of equation (4) by 11, get the equation：
        -1D = - 
12328
3759
    (21)
, then subtract both sides of equation (21) from both sides of equation (3), get the equation：
-1A + D = - 
1004
1253
    (1)
 B = - 
5300
3759
    (2)
 C = 
6880
1253
    (3)
- 
11
5
D = - 
135608
18795
    (4)
 E = 
1004
1253
    (5)
 F = 
8312
3759
    (6)

Multiply both sides of equation (4) by 5
Divide both sides of equation (4) by 11, get the equation：
        -1D = - 
12328
3759
    (22)
, then add the two sides of equation (22) to both sides of equation (1), get the equation：
-1A = - 
15340
3759
    (1)
 B = - 
5300
3759
    (2)
 C = 
6880
1253
    (3)
- 
11
5
D = - 
135608
18795
    (4)
 E = 
1004
1253
    (5)
 F = 
8312
3759
    (6)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
15340
3759
    (1)
 B = - 
5300
3759
    (2)
 C = 
6880
1253
    (3)
 D = 
12328
3759
    (4)
 E = 
1004
1253
    (5)
 F = 
8312
3759
    (6)


Therefore, the solution of the equation set is:
A = 
15340
3759
B = - 
5300
3759
C = 
6880
1253
D = 
12328
3759
E = 
1004
1253
F = 
8312
3759


Convert the solution of the equation set to decimals:
A = 4.080873
B = -1.409949
C = 5.490822
D = 3.279596
E = 0.801277
F = 2.211226

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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