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

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

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

Multiply both sides of equation (2) by 8, the equation can be obtained:
        -8B + 8C + 8D = 0    (9)
, then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
 A + B -1F = 0    (1)
-1B + C + D = 0    (2)
-1D -1E + F = 0    (3)
-8C -16D -2F = -40    (4)
 20B + 4C -10F = -20    (5)
-4C + 8D -8E = 20    (6)

Multiply both sides of equation (2) by 20, the equation can be obtained:
        -20B + 20C + 20D = 0    (10)
, then add the two sides of equation (10) to both sides of equation (5), the equations are reduced to:
 A + B -1F = 0    (1)
-1B + C + D = 0    (2)
-1D -1E + F = 0    (3)
-8C -16D -2F = -40    (4)
 24C + 20D -10F = -20    (5)
-4C + 8D -8E = 20    (6)

交After the exchange of equation (3) and equation (4)， the equation system becomes:
 A + B -1F = 0    (1)
-1B + C + D = 0    (2)
-8C -16D -2F = -40    (3)
-1D -1E + F = 0    (4)
 24C + 20D -10F = -20    (5)
-4C + 8D -8E = 20    (6)

Multiply both sides of equation (3) by 3, the equation can be obtained:
        -24C -48D -6F = -120    (11)
, then add the two sides of equation (11) to both sides of equation (5), the equations are reduced to:
 A + B -1F = 0    (1)
-1B + C + D = 0    (2)
-8C -16D -2F = -40    (3)
-1D -1E + F = 0    (4)
-28D -16F = -140    (5)
-4C + 8D -8E = 20    (6)

Divide the two sides of equation (3) by 2, the equation can be obtained:
        -4C -8D -1F = -20    (12)
, then subtract both sides of equation (12) from both sides of equation (6), the equations are reduced to:
 A + B -1F = 0    (1)
-1B + C + D = 0    (2)
-8C -16D -2F = -40    (3)
-1D -1E + F = 0    (4)
-28D -16F = -140    (5)
 16D -8E + F = 40    (6)

Multiply both sides of equation (4) by 28, the equation can be obtained:
        -28D -28E + 28F = 0    (13)
, then subtract both sides of equation (13) from both sides of equation (5), the equations are reduced to:
 A + B -1F = 0    (1)
-1B + C + D = 0    (2)
-8C -16D -2F = -40    (3)
-1D -1E + F = 0    (4)
 28E -44F = -140    (5)
 16D -8E + F = 40    (6)

Multiply both sides of equation (4) by 16, the equation can be obtained:
        -16D -16E + 16F = 0    (14)
, then add the two sides of equation (14) to both sides of equation (6), the equations are reduced to:
 A + B -1F = 0    (1)
-1B + C + D = 0    (2)
-8C -16D -2F = -40    (3)
-1D -1E + F = 0    (4)
 28E -44F = -140    (5)
-24E + 17F = 40    (6)

Multiply both sides of equation (5) by 6
Divide the two sides of equation (5) by 7, the equation can be obtained:
         24E - 
264
7
F = -120    (15)
, then add the two sides of equation (15) to both sides of equation (6), the equations are reduced to:
 A + B -1F = 0    (1)
-1B + C + D = 0    (2)
-8C -16D -2F = -40    (3)
-1D -1E + F = 0    (4)
 28E -44F = -140    (5)
- 
145
7
F = -80    (6)

Multiply both sides of equation (6) by 308
Divide both sides of equation (6) by 145, get the equation：
        -44F = - 
4928
29
    (16)
, then subtract both sides of equation (16) from both sides of equation (5), get the equation：
 A + B -1F = 0    (1)
-1B + C + D = 0    (2)
-8C -16D -2F = -40    (3)
-1D -1E + F = 0    (4)
 28E = 
868
29
    (5)
- 
145
7
F = -80    (6)

Multiply both sides of equation (6) by 7
Divide both sides of equation (6) by 145, get the equation：
        -1F = - 
112
29
    (17)
, then add the two sides of equation (17) to both sides of equation (4), get the equation：
 A + B -1F = 0    (1)
-1B + C + D = 0    (2)
-8C -16D -2F = -40    (3)
-1D -1E = - 
112
29
    (4)
 28E = 
868
29
    (5)
- 
145
7
F = -80    (6)

Multiply both sides of equation (6) by 14
Divide both sides of equation (6) by 145, get the equation：
        -2F = - 
224
29
    (18)
, then subtract both sides of equation (18) from both sides of equation (3), get the equation：
 A + B -1F = 0    (1)
-1B + C + D = 0    (2)
-8C -16D = - 
936
29
    (3)
-1D -1E = - 
112
29
    (4)
 28E = 
868
29
    (5)
- 
145
7
F = -80    (6)

Multiply both sides of equation (6) by 7
Divide both sides of equation (6) by 145, get the equation：
        -1F = - 
112
29
    (19)
, then subtract both sides of equation (19) from both sides of equation (1), get the equation：
 A + B = 
112
29
    (1)
-1B + C + D = 0    (2)
-8C -16D = - 
936
29
    (3)
-1D -1E = - 
112
29
    (4)
 28E = 
868
29
    (5)
- 
145
7
F = -80    (6)

Divide both sides of equation (5) by 28, get the equation：
         E = 
31
29
    (20)
, then add the two sides of equation (20) to both sides of equation (4), get the equation：
 A + B = 
112
29
    (1)
-1B + C + D = 0    (2)
-8C -16D = - 
936
29
    (3)
-1D = - 
81
29
    (4)
 28E = 
868
29
    (5)
 F = 
112
29
    (6)

Multiply both sides of equation (4) by 16, get the equation：
        -16D = - 
1296
29
    (21)
, then subtract both sides of equation (21) from both sides of equation (3), get the equation：
 A + B = 
112
29
    (1)
-1B + C + D = 0    (2)
-8C = 
360
29
    (3)
-1D = - 
81
29
    (4)
 E = 
31
29
    (5)
 F = 
112
29
    (6)

Add both sides of equation (4) to both sides of equation (2), get the equation：
 A + B = 
112
29
    (1)
-1B + C = - 
81
29
    (2)
-8C = 
360
29
    (3)
-1D = - 
81
29
    (4)
 E = 
31
29
    (5)
 F = 
112
29
    (6)

Divide both sides of equation (3) by 8, get the equation：
        -1C = 
45
29
    (22)
, then add the two sides of equation (22) to both sides of equation (2), get the equation：
 A + B = 
112
29
    (1)
-1B = - 
36
29
    (2)
-8C = 
360
29
    (3)
 D = 
81
29
    (4)
 E = 
31
29
    (5)
 F = 
112
29
    (6)

Add both sides of equation (2) to both sides of equation (1), get the equation：
 A = 
76
29
    (1)
-1B = - 
36
29
    (2)
 C = - 
45
29
    (3)
 D = 
81
29
    (4)
 E = 
31
29
    (5)
 F = 
112
29
    (6)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
76
29
    (1)
 B = 
36
29
    (2)
 C = - 
45
29
    (3)
 D = 
81
29
    (4)
 E = 
31
29
    (5)
 F = 
112
29
    (6)


Therefore, the solution of the equation set is:
A = 
76
29
B = 
36
29
C = - 
45
29
D = 
81
29
E = 
31
29
F = 
112
29


Convert the solution of the equation set to decimals:
A = 2.620690
B = 1.241379
C = -1.551724
D = 2.793103
E = 1.068966
F = 3.862069

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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