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

Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:
 A -1D -1F = 0    (1)
-1B + C -1D = 0    (2)
 B + D + E + F = 0    (3)
 4C + 10D -10F = -20    (4)
-8B -4C + 8E = 20    (5)
-2A + 8B -10D = -40    (6)

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

Add both sides of equation (2) to both sides of equation (3) ,the equations are reduced to:
 A -1D -1F = 0    (1)
-1B + C -1D = 0    (2)
 C + E + F = 0    (3)
 4C + 10D -10F = -20    (4)
-8B -4C + 8E = 20    (5)
 8B -12D -2F = -40    (6)

Multiply both sides of equation (2) by 8, the equation can be obtained:
        -8B + 8C -8D = 0    (8)
, then subtract both sides of equation (8) from both sides of equation (5), the equations are reduced to:
 A -1D -1F = 0    (1)
-1B + C -1D = 0    (2)
 C + E + F = 0    (3)
 4C + 10D -10F = -20    (4)
-12C + 8D + 8E = 20    (5)
 8B -12D -2F = -40    (6)

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

Multiply both sides of equation (3) by 4, the equation can be obtained:
         4C + 4E + 4F = 0    (10)
, then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
 A -1D -1F = 0    (1)
-1B + C -1D = 0    (2)
 C + E + F = 0    (3)
 10D -4E -14F = -20    (4)
-12C + 8D + 8E = 20    (5)
 8C -20D -2F = -40    (6)

Multiply both sides of equation (3) by 12, the equation can be obtained:
         12C + 12E + 12F = 0    (11)
, then add the two sides of equation (11) to both sides of equation (5), the equations are reduced to:
 A -1D -1F = 0    (1)
-1B + C -1D = 0    (2)
 C + E + F = 0    (3)
 10D -4E -14F = -20    (4)
 8D + 20E + 12F = 20    (5)
 8C -20D -2F = -40    (6)

Multiply both sides of equation (3) by 8, the equation can be obtained:
         8C + 8E + 8F = 0    (12)
, then subtract both sides of equation (12) from both sides of equation (6), the equations are reduced to:
 A -1D -1F = 0    (1)
-1B + C -1D = 0    (2)
 C + E + F = 0    (3)
 10D -4E -14F = -20    (4)
 8D + 20E + 12F = 20    (5)
-20D -8E -10F = -40    (6)

Multiply both sides of equation (4) by 4
Divide the two sides of equation (4) by 5, the equation can be obtained:
         8D - 
16
5
E - 
56
5
F = -16    (13)
, then subtract both sides of equation (13) from both sides of equation (5), the equations are reduced to:
 A -1D -1F = 0    (1)
-1B + C -1D = 0    (2)
 C + E + F = 0    (3)
 10D -4E -14F = -20    (4)
 
116
5
E + 
116
5
F = 36    (5)
-20D -8E -10F = -40    (6)

Multiply both sides of equation (4) by 2, the equation can be obtained:
         20D -8E -28F = -40    (14)
, then add the two sides of equation (14) to both sides of equation (6), the equations are reduced to:
 A -1D -1F = 0    (1)
-1B + C -1D = 0    (2)
 C + E + F = 0    (3)
 10D -4E -14F = -20    (4)
 
116
5
E + 
116
5
F = 36    (5)
-16E -38F = -80    (6)

Multiply both sides of equation (5) by 20
Divide the two sides of equation (5) by 29, the equation can be obtained:
         16E + 16F = 
720
29
    (15)
, then add the two sides of equation (15) to both sides of equation (6), the equations are reduced to:
 A -1D -1F = 0    (1)
-1B + C -1D = 0    (2)
 C + E + F = 0    (3)
 10D -4E -14F = -20    (4)
 
116
5
E + 
116
5
F = 36    (5)
-22F = - 
1600
29
    (6)

Multiply both sides of equation (6) by 58
Divide both sides of equation (6) by 55, get the equation：
        - 
116
5
F = - 
640
11
    (16)
, then add the two sides of equation (16) to both sides of equation (5), get the equation：
 A -1D -1F = 0    (1)
-1B + C -1D = 0    (2)
 C + E + F = 0    (3)
 10D -4E -14F = -20    (4)
 
116
5
E = - 
244
11
    (5)
-22F = - 
1600
29
    (6)

Multiply both sides of equation (6) by 7
Divide both sides of equation (6) by 11, get the equation：
        -14F = - 
11200
319
    (17)
, then subtract both sides of equation (17) from both sides of equation (4), get the equation：
 A -1D -1F = 0    (1)
-1B + C -1D = 0    (2)
 C + E + F = 0    (3)
 10D -4E = 
4820
319
    (4)
 
116
5
E = - 
244
11
    (5)
-22F = - 
1600
29
    (6)

Divide both sides of equation (6) by 22, get the equation：
        -1F = - 
800
319
    (18)
, then add the two sides of equation (18) to both sides of equation (3), get the equation：
 A -1D -1F = 0    (1)
-1B + C -1D = 0    (2)
 C + E = - 
800
319
    (3)
 10D -4E = 
4820
319
    (4)
 
116
5
E = - 
244
11
    (5)
-22F = - 
1600
29
    (6)

Divide both sides of equation (6) by 22, get the equation：
        -1F = - 
800
319
    (19)
, then subtract both sides of equation (19) from both sides of equation (1), get the equation：
 A -1D = 
800
319
    (1)
-1B + C -1D = 0    (2)
 C + E = - 
800
319
    (3)
 10D -4E = 
4820
319
    (4)
 
116
5
E = - 
244
11
    (5)
-22F = - 
1600
29
    (6)

Multiply both sides of equation (5) by 5
Divide both sides of equation (5) by 29, get the equation：
         4E = - 
1220
319
    (20)
, then add the two sides of equation (20) to both sides of equation (4), get the equation：
 A -1D = 
800
319
    (1)
-1B + C -1D = 0    (2)
 C + E = - 
800
319
    (3)
 10D = 
3600
319
    (4)
 
116
5
E = - 
244
11
    (5)
 F = 
800
319
    (6)

Multiply both sides of equation (5) by 5
Divide both sides of equation (5) by 116, get the equation：
         E = - 
305
319
    (21)
, then subtract both sides of equation (21) from both sides of equation (3), get the equation：
 A -1D = 
800
319
    (1)
-1B + C -1D = 0    (2)
 C = - 
45
29
    (3)
 10D = 
3600
319
    (4)
 
116
5
E = - 
244
11
    (5)
 F = 
800
319
    (6)

Divide both sides of equation (4) by 10, get the equation：
         D = 
360
319
    (22)
, then add the two sides of equation (22) to both sides of equation (2), get the equation：
 A -1D = 
800
319
    (1)
-1B + C = 
360
319
    (2)
 C = - 
45
29
    (3)
 10D = 
3600
319
    (4)
 E = - 
305
319
    (5)
 F = 
800
319
    (6)

Divide both sides of equation (4) by 10, get the equation：
         D = 
360
319
    (23)
, then add the two sides of equation (23) to both sides of equation (1), get the equation：
 A = 
1160
319
    (1)
-1B + C = 
360
319
    (2)
 C = - 
45
29
    (3)
 10D = 
3600
319
    (4)
 E = - 
305
319
    (5)
 F = 
800
319
    (6)

Subtract both sides of equation (3) from both sides of equation (2), get the equation：
 A = 
1160
319
    (1)
-1B = 
855
319
    (2)
 C = - 
45
29
    (3)
 D = 
360
319
    (4)
 E = - 
305
319
    (5)
 F = 
800
319
    (6)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
1160
319
    (1)
 B = - 
855
319
    (2)
 C = - 
45
29
    (3)
 D = 
360
319
    (4)
 E = - 
305
319
    (5)
 F = 
800
319
    (6)


Therefore, the solution of the equation set is:
A = 
1160
319
B = - 
855
319
C = - 
45
29
D = 
360
319
E = - 
305
319
F = 
800
319


Convert the solution of the equation set to decimals:
A = 3.636364
B = -2.680251
C = -1.551724
D = 1.128527
E = -0.956113
F = 2.507837

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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