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

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

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

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

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

Add both sides of equation (3) to both sides of equation (4) ,the equations are reduced to:
 A -1B -1F = 0    (1)
 B + C -1D = 0    (2)
 C + E -1F = 0    (3)
0 = 0    (4)
-20C + 24D + 10F = -20    (5)
-8C -4D + 8E = 20    (6)

Multiply both sides of equation (3) by 20, the equation can be obtained:
         20C + 20E -20F = 0    (9)
, then add the two sides of equation (9) to both sides of equation (5), the equations are reduced to:
 A -1B -1F = 0    (1)
 B + C -1D = 0    (2)
 C + E -1F = 0    (3)
0 = 0    (4)
 24D + 20E -10F = -20    (5)
-8C -4D + 8E = 20    (6)

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

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

Divide the two sides of equation (4) by 6, the equation can be obtained:
         4D + 
10
3
E - 
5
3
F = - 
10
3
    (11)
, then add the two sides of equation (11) to both sides of equation (6), the equations are reduced to:
 A -1B -1F = 0    (1)
 B + C -1D = 0    (2)
 C + E -1F = 0    (3)
 24D + 20E -10F = -20    (4)
0 = 0    (5)
 
58
3
E - 
29
3
F = 
50
3
    (6)

交After the exchange of equation (5) and equation (6)， the equation system becomes:
 A -1B -1F = 0    (1)
 B + C -1D = 0    (2)
 C + E -1F = 0    (3)
 24D + 20E -10F = -20    (4)
 
58
3
E - 
29
3
F = 
50
3
    (5)
0 = 0    (6)

Multiply both sides of equation (5) by 30
Divide both sides of equation (5) by 29, get the equation：
         20E -10F = 
500
29
    (12)
, then subtract both sides of equation (12) from both sides of equation (4), get the equation：
 A -1B -1F = 0    (1)
 B + C -1D = 0    (2)
 C + E -1F = 0    (3)
 24D = - 
1080
29
    (4)
 
58
3
E - 
29
3
F = 
50
3
    (5)
0 = 0    (6)

Multiply both sides of equation (5) by 3
Divide both sides of equation (5) by 58, get the equation：
         E - 
1
2
F = 
25
29
    (13)
, then subtract both sides of equation (13) from both sides of equation (3), get the equation：
 A -1B -1F = 0    (1)
 B + C -1D = 0    (2)
 C - 
1
2
F = - 
25
29
    (3)
 24D = - 
1080
29
    (4)
 
58
3
E - 
29
3
F = 
50
3
    (5)
0 = 0    (6)

Divide both sides of equation (4) by 24, get the equation：
         D = - 
45
29
    (14)
, then add the two sides of equation (14) to both sides of equation (2), get the equation：
 A -1B -1F = 0    (1)
 B + C = - 
45
29
    (2)
 C - 
1
2
F = - 
25
29
    (3)
 24D = - 
1080
29
    (4)
 E - 
1
2
F = 
25
29
    (5)
0 = 0    (6)

Subtract both sides of equation (3) from both sides of equation (2), get the equation：
 A -1B -1F = 0    (1)
 B + 
1
2
F = - 
20
29
    (2)
 C - 
1
2
F = - 
25
29
    (3)
 D = - 
45
29
    (4)
 E - 
1
2
F = 
25
29
    (5)
0 = 0    (6)

Add both sides of equation (2) to both sides of equation (1), get the equation：
 A - 
1
2
F = - 
20
29
    (1)
 B + 
1
2
F = - 
20
29
    (2)
 C - 
1
2
F = - 
25
29
    (3)
 D = - 
45
29
    (4)
 E - 
1
2
F = 
25
29
    (5)
0 = 0    (6)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A - 
1
2
F = - 
20
29
    (1)
 B + 
1
2
F = - 
20
29
    (2)
 C - 
1
2
F = - 
25
29
    (3)
 D = - 
45
29
    (4)
 E - 
1
2
F = 
25
29
    (5)
0 = 0    (6)


Therefore, the solution of the equation set is:
A = - 
20
29
 + 
1
2
F
B = - 
20
29
 - 
1
2
F
C = - 
25
29
 + 
1
2
F
D = - 
45
29
E = 
25
29
 + 
1
2
F


Convert the solution of the equation set to decimals:
A = -0.689655 + 
1
2
F
B = -0.689655 - 
1
2
F
C = -0.862069 + 
1
2
F
D = -1.551724
E = 0.862069 + 
1
2
F

Where:  F are arbitrary constants.
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