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

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

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

Multiply both sides of equation (2) by 5, the equation can be obtained:
         5B + 5C -5D = 0    (9)
, then add the two sides of equation (9) to both sides of equation (6), the equations are reduced to:
-1A + D + E = 0    (1)
 B + C -1D = 0    (2)
 D + E -1F = 0    (3)
-5C + 9D + F = -20    (4)
-1C -2D + 2E = 5    (5)
 7C + 5E = -10    (6)

交After the exchange of equation (3) and equation (4)， the equation system becomes:
-1A + D + E = 0    (1)
 B + C -1D = 0    (2)
-5C + 9D + F = -20    (3)
 D + E -1F = 0    (4)
-1C -2D + 2E = 5    (5)
 7C + 5E = -10    (6)

Divide the two sides of equation (3) by 5, the equation can be obtained:
        -1C + 
9
5
D + 
1
5
F = -4    (10)
, then subtract both sides of equation (10) from both sides of equation (5), the equations are reduced to:
-1A + D + E = 0    (1)
 B + C -1D = 0    (2)
-5C + 9D + F = -20    (3)
 D + E -1F = 0    (4)
- 
19
5
D + 2E - 
1
5
F = 9    (5)
 7C + 5E = -10    (6)

Multiply both sides of equation (3) by 7
Divide the two sides of equation (3) by 5, the equation can be obtained:
        -7C + 
63
5
D + 
7
5
F = -28    (11)
, then add the two sides of equation (11) to both sides of equation (6), the equations are reduced to:
-1A + D + E = 0    (1)
 B + C -1D = 0    (2)
-5C + 9D + F = -20    (3)
 D + E -1F = 0    (4)
- 
19
5
D + 2E - 
1
5
F = 9    (5)
 
63
5
D + 5E + 
7
5
F = -38    (6)

Multiply both sides of equation (4) by 19
Divide the two sides of equation (4) by 5, the equation can be obtained:
         
19
5
D + 
19
5
E - 
19
5
F = 0    (12)
, then add the two sides of equation (12) to both sides of equation (5), the equations are reduced to:
-1A + D + E = 0    (1)
 B + C -1D = 0    (2)
-5C + 9D + F = -20    (3)
 D + E -1F = 0    (4)
 
29
5
E -4F = 9    (5)
 
63
5
D + 5E + 
7
5
F = -38    (6)

Multiply both sides of equation (4) by 63
Divide the two sides of equation (4) by 5, the equation can be obtained:
         
63
5
D + 
63
5
E - 
63
5
F = 0    (13)
, then subtract both sides of equation (13) from both sides of equation (6), the equations are reduced to:
-1A + D + E = 0    (1)
 B + C -1D = 0    (2)
-5C + 9D + F = -20    (3)
 D + E -1F = 0    (4)
 
29
5
E -4F = 9    (5)
- 
38
5
E + 14F = -38    (6)

Multiply both sides of equation (5) by 38
Divide the two sides of equation (5) by 29, the equation can be obtained:
         
38
5
E - 
152
29
F = 
342
29
    (14)
, then add the two sides of equation (14) to both sides of equation (6), the equations are reduced to:
-1A + D + E = 0    (1)
 B + C -1D = 0    (2)
-5C + 9D + F = -20    (3)
 D + E -1F = 0    (4)
 
29
5
E -4F = 9    (5)
 
254
29
F = - 
760
29
    (6)

Multiply both sides of equation (6) by 58
Divide both sides of equation (6) by 127, get the equation：
         
508
127
F = - 
1520
127
    (15)
, then add the two sides of equation (15) to both sides of equation (5), get the equation：
-1A + D + E = 0    (1)
 B + C -1D = 0    (2)
-5C + 9D + F = -20    (3)
 D + E -1F = 0    (4)
 
29
5
E = - 
377
127
    (5)
 
254
29
F = - 
760
29
    (6)

Multiply both sides of equation (6) by 29
Divide both sides of equation (6) by 254, get the equation：
         F = - 
380
127
    (16)
, then add the two sides of equation (16) to both sides of equation (4), get the equation：
-1A + D + E = 0    (1)
 B + C -1D = 0    (2)
-5C + 9D + F = -20    (3)
 D + E = - 
380
127
    (4)
 
29
5
E = - 
377
127
    (5)
 
254
29
F = - 
760
29
    (6)

Multiply both sides of equation (6) by 29
Divide both sides of equation (6) by 254, get the equation：
         F = - 
380
127
    (17)
, then subtract both sides of equation (17) from both sides of equation (3), get the equation：
-1A + D + E = 0    (1)
 B + C -1D = 0    (2)
-5C + 9D = - 
2160
127
    (3)
 D + E = - 
380
127
    (4)
 
29
5
E = - 
377
127
    (5)
 
254
29
F = - 
760
29
    (6)

Multiply both sides of equation (5) by 5
Divide both sides of equation (5) by 29, get the equation：
         E = - 
65
127
    (18)
, then subtract both sides of equation (18) from both sides of equation (4), get the equation：
-1A + D + E = 0    (1)
 B + C -1D = 0    (2)
-5C + 9D = - 
2160
127
    (3)
 D = - 
315
127
    (4)
 
29
5
E = - 
377
127
    (5)
 F = - 
380
127
    (6)

Multiply both sides of equation (5) by 5
Divide both sides of equation (5) by 29, get the equation：
         E = - 
65
127
    (19)
, then subtract both sides of equation (19) from both sides of equation (1), get the equation：
-1A + D = 
65
127
    (1)
 B + C -1D = 0    (2)
-5C + 9D = - 
2160
127
    (3)
 D = - 
315
127
    (4)
 
29
5
E = - 
377
127
    (5)
 F = - 
380
127
    (6)

Multiply both sides of equation (4) by 9, get the equation：
         9D = - 
2835
127
    (20)
, then subtract both sides of equation (20) from both sides of equation (3), get the equation：
-1A + D = 
65
127
    (1)
 B + C -1D = 0    (2)
-5C = 
675
127
    (3)
 D = - 
315
127
    (4)
 E = - 
65
127
    (5)
 F = - 
380
127
    (6)

Add both sides of equation (4) to both sides of equation (2), get the equation：
-1A + D = 
65
127
    (1)
 B + C = - 
315
127
    (2)
-5C = 
675
127
    (3)
 D = - 
315
127
    (4)
 E = - 
65
127
    (5)
 F = - 
380
127
    (6)

Subtract both sides of equation (4) from both sides of equation (1), get the equation：
-1A = 
380
127
    (1)
 B + C = - 
315
127
    (2)
-5C = 
675
127
    (3)
 D = - 
315
127
    (4)
 E = - 
65
127
    (5)
 F = - 
380
127
    (6)

Divide both sides of equation (3) by 5, get the equation：
        -1C = 
135
127
    (21)
, then add the two sides of equation (21) to both sides of equation (2), get the equation：
-1A = 
380
127
    (1)
 B = - 
180
127
    (2)
-5C = 
675
127
    (3)
 D = - 
315
127
    (4)
 E = - 
65
127
    (5)
 F = - 
380
127
    (6)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = - 
380
127
    (1)
 B = - 
180
127
    (2)
 C = - 
135
127
    (3)
 D = - 
315
127
    (4)
 E = - 
65
127
    (5)
 F = - 
380
127
    (6)


Therefore, the solution of the equation set is:
A = - 
380
127
B = - 
180
127
C = - 
135
127
D = - 
315
127
E = - 
65
127
F = - 
380
127


Convert the solution of the equation set to decimals:
A = -2.992126
B = -1.417323
C = -1.062992
D = -2.480315
E = -0.511811
F = -2.992126

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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