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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:
 12A + 12B + 2C + 3D + 4E + 2F = 
4329
5
    (1)
 12A + 12B + C + 2D + 3E + F = 
6151
10
    (2)
 10A + 10B + C + 2D + 3E + 2F = 
2507
4
    (3)
 A + 10B + C + 2E + F = 
2507
5
    (4)
 E = 35    (5)
 F = 12    (6)
Question solving process:

Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
 12A + 12B + 2C + 3D + 4E + 2F = 
4329
5
    (1)
-1C -1D -1E -1F = - 
2507
10
    (2)
 10A + 10B + C + 2D + 3E + 2F = 
2507
4
    (3)
 A + 10B + C + 2E + F = 
2507
5
    (4)
 E = 35    (5)
 F = 12    (6)

Multiply both sides of equation (1) by 5
Divide the two sides of equation (1) by 6, the equation can be obtained:
         10A + 10B + 
5
3
C + 
5
2
D + 
10
3
E + 
5
3
F = 
1443
2
    (7)
, then subtract both sides of equation (7) from both sides of equation (3), the equations are reduced to:
 12A + 12B + 2C + 3D + 4E + 2F = 
4329
5
    (1)
-1C -1D -1E -1F = - 
2507
10
    (2)
- 
2
3
C - 
1
2
D - 
1
3
E + 
1
3
F = - 
379
4
    (3)
 A + 10B + C + 2E + F = 
2507
5
    (4)
 E = 35    (5)
 F = 12    (6)

Divide the two sides of equation (1) by 12, the equation can be obtained:
         A + B + 
1
6
C + 
1
4
D + 
1
3
E + 
1
6
F = 
1443
20
    (8)
, then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
 12A + 12B + 2C + 3D + 4E + 2F = 
4329
5
    (1)
-1C -1D -1E -1F = - 
2507
10
    (2)
- 
2
3
C - 
1
2
D - 
1
3
E + 
1
3
F = - 
379
4
    (3)
 9B + 
5
6
C - 
1
4
D + 
5
3
E + 
5
6
F = 
1717
4
    (4)
 E = 35    (5)
 F = 12    (6)

交After the exchange of equation (2) and equation (4)， the equation system becomes:
 12A + 12B + 2C + 3D + 4E + 2F = 
4329
5
    (1)
 9B + 
5
6
C - 
1
4
D + 
5
3
E + 
5
6
F = 
1717
4
    (2)
- 
2
3
C - 
1
2
D - 
1
3
E + 
1
3
F = - 
379
4
    (3)
-1C -1D -1E -1F = - 
2507
10
    (4)
 E = 35    (5)
 F = 12    (6)

Multiply both sides of equation (3) by 3
Divide the two sides of equation (3) by 2, the equation can be obtained:
        -1C - 
3
4
D - 
1
2
E + 
1
2
F = - 
1137
8
    (9)
, then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
 12A + 12B + 2C + 3D + 4E + 2F = 
4329
5
    (1)
 9B + 
5
6
C - 
1
4
D + 
5
3
E + 
5
6
F = 
1717
4
    (2)
- 
2
3
C - 
1
2
D - 
1
3
E + 
1
3
F = - 
379
4
    (3)
- 
1
4
D - 
1
2
E - 
3
2
F = - 
4343
40
    (4)
 E = 35    (5)
 F = 12    (6)

Multiply both sides of equation (6) by 3
Divide both sides of equation (6) by 2, get the equation：
         
3
2
F = 18    (10)
, then add the two sides of equation (10) to both sides of equation (4), get the equation：
 12A + 12B + 2C + 3D + 4E + 2F = 
4329
5
    (1)
 9B + 
5
6
C - 
1
4
D + 
5
3
E + 
5
6
F = 
1717
4
    (2)
- 
2
3
C - 
1
2
D - 
1
3
E + 
1
3
F = - 
379
4
    (3)
- 
1
4
D - 
1
2
E = - 
3623
40
    (4)
 E = 35    (5)
 F = 12    (6)

Divide both sides of equation (6) by 3, get the equation：
         
1
3
F = 4    (11)
, then subtract both sides of equation (11) from both sides of equation (3), get the equation：
 12A + 12B + 2C + 3D + 4E + 2F = 
4329
5
    (1)
 9B + 
5
6
C - 
1
4
D + 
5
3
E + 
5
6
F = 
1717
4
    (2)
- 
2
3
C - 
1
2
D - 
1
3
E = - 
395
4
    (3)
- 
1
4
D - 
1
2
E = - 
3623
40
    (4)
 E = 35    (5)
 F = 12    (6)

Multiply both sides of equation (6) by 5
Divide both sides of equation (6) by 6, get the equation：
         
5
6
F = 10    (12)
, then subtract both sides of equation (12) from both sides of equation (2), get the equation：
 12A + 12B + 2C + 3D + 4E + 2F = 
4329
5
    (1)
 9B + 
5
6
C - 
1
4
D + 
5
3
E = 
1677
4
    (2)
- 
2
3
C - 
1
2
D - 
1
3
E = - 
395
4
    (3)
- 
1
4
D - 
1
2
E = - 
3623
40
    (4)
 E = 35    (5)
 F = 12    (6)

Multiply both sides of equation (6) by 2, get the equation：
         2F = 24    (13)
, then subtract both sides of equation (13) from both sides of equation (1), get the equation：
 12A + 12B + 2C + 3D + 4E = 
4209
5
    (1)
 9B + 
5
6
C - 
1
4
D + 
5
3
E = 
1677
4
    (2)
- 
2
3
C - 
1
2
D - 
1
3
E = - 
395
4
    (3)
- 
1
4
D - 
1
2
E = - 
3623
40
    (4)
 E = 35    (5)
 F = 12    (6)

Divide both sides of equation (5) by 2, get the equation：
         
1
2
E = 
35
2
    (14)
, then add the two sides of equation (14) to both sides of equation (4), get the equation：
 12A + 12B + 2C + 3D + 4E = 
4209
5
    (1)
 9B + 
5
6
C - 
1
4
D + 
5
3
E = 
1677
4
    (2)
- 
2
3
C - 
1
2
D - 
1
3
E = - 
395
4
    (3)
- 
1
4
D = - 
2923
40
    (4)
 E = 35    (5)
 F = 12    (6)

Divide both sides of equation (5) by 3, get the equation：
         
1
3
E = 
35
3
    (15)
, then add the two sides of equation (15) to both sides of equation (3), get the equation：
 12A + 12B + 2C + 3D + 4E = 
4209
5
    (1)
 9B + 
5
6
C - 
1
4
D + 
5
3
E = 
1677
4
    (2)
- 
2
3
C - 
1
2
D = - 
1045
12
    (3)
- 
1
4
D = - 
2923
40
    (4)
 E = 35    (5)
 F = 12    (6)

Multiply both sides of equation (5) by 5
Divide both sides of equation (5) by 3, get the equation：
         
5
3
E = 
175
3
    (16)
, then subtract both sides of equation (16) from both sides of equation (2), get the equation：
 12A + 12B + 2C + 3D + 4E = 
4209
5
    (1)
 9B + 
5
6
C - 
1
4
D = 
4331
12
    (2)
- 
2
3
C - 
1
2
D = - 
1045
12
    (3)
- 
1
4
D = - 
2923
40
    (4)
 E = 35    (5)
 F = 12    (6)

Multiply both sides of equation (5) by 4, get the equation：
         4E = 140    (17)
, then subtract both sides of equation (17) from both sides of equation (1), get the equation：
 12A + 12B + 2C + 3D = 
3509
5
    (1)
 9B + 
5
6
C - 
1
4
D = 
4331
12
    (2)
- 
2
3
C - 
1
2
D = - 
1045
12
    (3)
- 
1
4
D = - 
2923
40
    (4)
 E = 35    (5)
 F = 12    (6)

Multiply both sides of equation (4) by 2, get the equation：
        - 
1
2
D = - 
2923
20
    (18)
, then subtract both sides of equation (18) from both sides of equation (3), get the equation：
 12A + 12B + 2C + 3D = 
3509
5
    (1)
 9B + 
5
6
C - 
1
4
D = 
4331
12
    (2)
- 
2
3
C = 
886
15
    (3)
- 
1
4
D = - 
2923
40
    (4)
 E = 35    (5)
 F = 12    (6)

Subtract both sides of equation (4) from both sides of equation (2), get the equation：
 12A + 12B + 2C + 3D = 
3509
5
    (1)
 9B + 
5
6
C = 
52079
120
    (2)
- 
2
3
C = 
886
15
    (3)
- 
1
4
D = - 
2923
40
    (4)
 E = 35    (5)
 F = 12    (6)

Multiply both sides of equation (4) by 12, get the equation：
        -3D = - 
8769
10
    (19)
, then add the two sides of equation (19) to both sides of equation (1), get the equation：
 12A + 12B + 2C = - 
1751
10
    (1)
 9B + 
5
6
C = 
52079
120
    (2)
- 
2
3
C = 
886
15
    (3)
- 
1
4
D = - 
2923
40
    (4)
 E = 35    (5)
 F = 12    (6)

Multiply both sides of equation (3) by 5
Divide both sides of equation (3) by 4, get the equation：
        - 
5
6
C = 
443
6
    (20)
, then add the two sides of equation (20) to both sides of equation (2), get the equation：
 12A + 12B + 2C = - 
1751
10
    (1)
 9B = 
20313
40
    (2)
- 
2
3
C = 
886
15
    (3)
 D = 
2923
10
    (4)
 E = 35    (5)
 F = 12    (6)

Multiply both sides of equation (3) by 3, get the equation：
        -2C = 
886
5
    (21)
, then add the two sides of equation (21) to both sides of equation (1), get the equation：
 12A + 12B = 
21
10
    (1)
 9B = 
20313
40
    (2)
- 
2
3
C = 
886
15
    (3)
 D = 
2923
10
    (4)
 E = 35    (5)
 F = 12    (6)

Multiply both sides of equation (2) by 4
Divide both sides of equation (2) by 3, get the equation：
         12B = 
6771
10
    (22)
, then subtract both sides of equation (22) from both sides of equation (1), get the equation：
 12A = -675    (1)
 9B = 
20313
40
    (2)
 C = - 
443
5
    (3)
 D = 
2923
10
    (4)
 E = 35    (5)
 F = 12    (6)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = - 
225
4
    (1)
 B = 
2257
40
    (2)
 C = - 
443
5
    (3)
 D = 
2923
10
    (4)
 E = 35    (5)
 F = 12    (6)


Therefore, the solution of the equation set is:
A = - 
225
4
B = 
2257
40
C = - 
443
5
D = 
2923
10
E = 35
F = 12


Convert the solution of the equation set to decimals:
A = -56.250000
B = 56.425000
C = -88.600000
D = 292.300000
E = 35
F = 12

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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