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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:
 2A + 2B + C + 2D + 2E + 2F = 
4329
5
    (1)
 2A + B + 
1
2
C + 2D + 2E + 2F = 
6151
10
    (2)
 2A + 2B + 
1
2
C + 2D + 2E + F = 
6267
10
    (3)
 A + 2D + 2E + F = 
5017
10
    (4)
 E = 55    (5)
 F = 15    (6)
Question solving process:

Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
 2A + 2B + C + 2D + 2E + 2F = 
4329
5
    (1)
-1B - 
1
2
C = - 
2507
10
    (2)
 2A + 2B + 
1
2
C + 2D + 2E + F = 
6267
10
    (3)
 A + 2D + 2E + F = 
5017
10
    (4)
 E = 55    (5)
 F = 15    (6)

Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:
 2A + 2B + C + 2D + 2E + 2F = 
4329
5
    (1)
-1B - 
1
2
C = - 
2507
10
    (2)
- 
1
2
C -1F = - 
2391
10
    (3)
 A + 2D + 2E + F = 
5017
10
    (4)
 E = 55    (5)
 F = 15    (6)

Divide the two sides of equation (1) by 2, the equation can be obtained:
         A + B + 
1
2
C + D + E + F = 
4329
10
    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 2A + 2B + C + 2D + 2E + 2F = 
4329
5
    (1)
-1B - 
1
2
C = - 
2507
10
    (2)
- 
1
2
C -1F = - 
2391
10
    (3)
-1B - 
1
2
C + D + E = 
344
5
    (4)
 E = 55    (5)
 F = 15    (6)

Subtract both sides of equation (2) from both sides of equation (4) ,the equations are reduced to:
 2A + 2B + C + 2D + 2E + 2F = 
4329
5
    (1)
-1B - 
1
2
C = - 
2507
10
    (2)
- 
1
2
C -1F = - 
2391
10
    (3)
 D + E = 
639
2
    (4)
 E = 55    (5)
 F = 15    (6)

Add both sides of equation (6) to both sides of equation (3), get the equation：
 2A + 2B + C + 2D + 2E + 2F = 
4329
5
    (1)
-1B - 
1
2
C = - 
2507
10
    (2)
- 
1
2
C = - 
2241
10
    (3)
 D + E = 
639
2
    (4)
 E = 55    (5)
 F = 15    (6)

Multiply both sides of equation (6) by 2, get the equation：
         2F = 30    (8)
, then subtract both sides of equation (8) from both sides of equation (1), get the equation：
 2A + 2B + C + 2D + 2E = 
4179
5
    (1)
-1B - 
1
2
C = - 
2507
10
    (2)
- 
1
2
C = - 
2241
10
    (3)
 D + E = 
639
2
    (4)
 E = 55    (5)
 F = 15    (6)

Subtract both sides of equation (5) from both sides of equation (4), get the equation：
 2A + 2B + C + 2D + 2E = 
4179
5
    (1)
-1B - 
1
2
C = - 
2507
10
    (2)
- 
1
2
C = - 
2241
10
    (3)
 D = 
529
2
    (4)
 E = 55    (5)
 F = 15    (6)

Multiply both sides of equation (5) by 2, get the equation：
         2E = 110    (9)
, then subtract both sides of equation (9) from both sides of equation (1), get the equation：
 2A + 2B + C + 2D = 
3629
5
    (1)
-1B - 
1
2
C = - 
2507
10
    (2)
- 
1
2
C = - 
2241
10
    (3)
 D = 
529
2
    (4)
 E = 55    (5)
 F = 15    (6)

Multiply both sides of equation (4) by 2, get the equation：
         2D = 529    (10)
, then subtract both sides of equation (10) from both sides of equation (1), get the equation：
 2A + 2B + C = 
984
5
    (1)
-1B - 
1
2
C = - 
2507
10
    (2)
- 
1
2
C = - 
2241
10
    (3)
 D = 
529
2
    (4)
 E = 55    (5)
 F = 15    (6)

Subtract both sides of equation (3) from both sides of equation (2), get the equation：
 2A + 2B + C = 
984
5
    (1)
-1B = - 
133
5
    (2)
- 
1
2
C = - 
2241
10
    (3)
 D = 
529
2
    (4)
 E = 55    (5)
 F = 15    (6)

Multiply both sides of equation (3) by 2, get the equation：
        -1C = - 
2241
5
    (11)
, then add the two sides of equation (11) to both sides of equation (1), get the equation：
 2A + 2B = - 
1257
5
    (1)
-1B = - 
133
5
    (2)
- 
1
2
C = - 
2241
10
    (3)
 D = 
529
2
    (4)
 E = 55    (5)
 F = 15    (6)

Multiply both sides of equation (2) by 2, get the equation：
        -2B = - 
266
5
    (12)
, then add the two sides of equation (12) to both sides of equation (1), get the equation：
 2A = - 
1523
5
    (1)
-1B = - 
133
5
    (2)
 C = 
2241
5
    (3)
 D = 
529
2
    (4)
 E = 55    (5)
 F = 15    (6)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = - 
1523
10
    (1)
 B = 
133
5
    (2)
 C = 
2241
5
    (3)
 D = 
529
2
    (4)
 E = 55    (5)
 F = 15    (6)


Therefore, the solution of the equation set is:
A = - 
1523
10
B = 
133
5
C = 
2241
5
D = 
529
2
E = 55
F = 15


Convert the solution of the equation set to decimals:
A = -152.300000
B = 26.600000
C = 448.200000
D = 264.500000
E = 55
F = 15

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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