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

Multiply both sides of equation (1) by 4, the equation can be obtained:
         4A -12B + 8D = -2    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 A -3B + 2D = - 
1
2
    (1)
 6E = 1    (2)
 8B -4C = -1    (3)
 11B -3C -8D + 2E = 2    (4)
-3B + D -3E + 2F = 0    (5)
-3C + 4D -2E = 0    (6)

交After the exchange of equation (2) and equation (3)， the equation system becomes:
 A -3B + 2D = - 
1
2
    (1)
 8B -4C = -1    (2)
 6E = 1    (3)
 11B -3C -8D + 2E = 2    (4)
-3B + D -3E + 2F = 0    (5)
-3C + 4D -2E = 0    (6)

Multiply both sides of equation (2) by 11
Divide the two sides of equation (2) by 8, the equation can be obtained:
         11B - 
11
2
C = - 
11
8
    (8)
, then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
 A -3B + 2D = - 
1
2
    (1)
 8B -4C = -1    (2)
 6E = 1    (3)
 
5
2
C -8D + 2E = 
27
8
    (4)
-3B + D -3E + 2F = 0    (5)
-3C + 4D -2E = 0    (6)

Multiply both sides of equation (2) by 3
Divide the two sides of equation (2) by 8, the equation can be obtained:
         3B - 
3
2
C = - 
3
8
    (9)
, then add the two sides of equation (9) to both sides of equation (5), the equations are reduced to:
 A -3B + 2D = - 
1
2
    (1)
 8B -4C = -1    (2)
 6E = 1    (3)
 
5
2
C -8D + 2E = 
27
8
    (4)
- 
3
2
C + D -3E + 2F = - 
3
8
    (5)
-3C + 4D -2E = 0    (6)

交After the exchange of equation (3) and equation (4)， the equation system becomes:
 A -3B + 2D = - 
1
2
    (1)
 8B -4C = -1    (2)
 
5
2
C -8D + 2E = 
27
8
    (3)
 6E = 1    (4)
- 
3
2
C + D -3E + 2F = - 
3
8
    (5)
-3C + 4D -2E = 0    (6)

Multiply both sides of equation (3) by 3
Divide the two sides of equation (3) by 5, the equation can be obtained:
         
3
2
C - 
24
5
D + 
6
5
E = 
81
40
    (10)
, then add the two sides of equation (10) to both sides of equation (5), the equations are reduced to:
 A -3B + 2D = - 
1
2
    (1)
 8B -4C = -1    (2)
 
5
2
C -8D + 2E = 
27
8
    (3)
 6E = 1    (4)
- 
19
5
D - 
9
5
E + 2F = 
33
20
    (5)
-3C + 4D -2E = 0    (6)

Multiply both sides of equation (3) by 6
Divide the two sides of equation (3) by 5, the equation can be obtained:
         3C - 
48
5
D + 
12
5
E = 
81
20
    (11)
, then add the two sides of equation (11) to both sides of equation (6), the equations are reduced to:
 A -3B + 2D = - 
1
2
    (1)
 8B -4C = -1    (2)
 
5
2
C -8D + 2E = 
27
8
    (3)
 6E = 1    (4)
- 
19
5
D - 
9
5
E + 2F = 
33
20
    (5)
- 
28
5
D + 
2
5
E = 
81
20
    (6)

交After the exchange of equation (4) and equation (5)， the equation system becomes:
 A -3B + 2D = - 
1
2
    (1)
 8B -4C = -1    (2)
 
5
2
C -8D + 2E = 
27
8
    (3)
- 
19
5
D - 
9
5
E + 2F = 
33
20
    (4)
 6E = 1    (5)
- 
28
5
D + 
2
5
E = 
81
20
    (6)

Multiply both sides of equation (4) by 28
Divide the two sides of equation (4) by 19, the equation can be obtained:
        - 
28
5
D - 
252
95
E + 
56
19
F = 
231
95
    (12)
, then subtract both sides of equation (12) from both sides of equation (6), the equations are reduced to:
 A -3B + 2D = - 
1
2
    (1)
 8B -4C = -1    (2)
 
5
2
C -8D + 2E = 
27
8
    (3)
- 
19
5
D - 
9
5
E + 2F = 
33
20
    (4)
 6E = 1    (5)
 
58
19
E - 
56
19
F = 
123
76
    (6)

Multiply both sides of equation (5) by 29
Divide the two sides of equation (5) by 57, the equation can be obtained:
         
58
19
E = 
29
57
    (13)
, then subtract both sides of equation (13) from both sides of equation (6), the equations are reduced to:
 A -3B + 2D = - 
1
2
    (1)
 8B -4C = -1    (2)
 
5
2
C -8D + 2E = 
27
8
    (3)
- 
19
5
D - 
9
5
E + 2F = 
33
20
    (4)
 6E = 1    (5)
- 
56
19
F = 
253
228
    (6)

Multiply both sides of equation (6) by 19
Divide both sides of equation (6) by 28, get the equation：
        -2F = 
253
336
    (14)
, then add the two sides of equation (14) to both sides of equation (4), get the equation：
 A -3B + 2D = - 
1
2
    (1)
 8B -4C = -1    (2)
 
5
2
C -8D + 2E = 
27
8
    (3)
- 
19
5
D - 
9
5
E = 
4037
1680
    (4)
 6E = 1    (5)
- 
56
19
F = 
253
228
    (6)

Multiply both sides of equation (5) by 3
Divide both sides of equation (5) by 10, get the equation：
         
9
5
E = 
3
10
    (15)
, then add the two sides of equation (15) to both sides of equation (4), get the equation：
 A -3B + 2D = - 
1
2
    (1)
 8B -4C = -1    (2)
 
5
2
C -8D + 2E = 
27
8
    (3)
- 
19
5
D = 
4541
1680
    (4)
 6E = 1    (5)
 F = - 
253
672
    (6)

Divide both sides of equation (5) by 3, get the equation：
         2E = 
1
3
    (16)
, then subtract both sides of equation (16) from both sides of equation (3), get the equation：
 A -3B + 2D = - 
1
2
    (1)
 8B -4C = -1    (2)
 
5
2
C -8D = 
73
24
    (3)
- 
19
5
D = 
4541
1680
    (4)
 6E = 1    (5)
 F = - 
253
672
    (6)

Multiply both sides of equation (4) by 40
Divide both sides of equation (4) by 19, get the equation：
        -8D = 
239
42
    (17)
, then subtract both sides of equation (17) from both sides of equation (3), get the equation：
 A -3B + 2D = - 
1
2
    (1)
 8B -4C = -1    (2)
 
5
2
C = - 
445
168
    (3)
- 
19
5
D = 
4541
1680
    (4)
 E = 
1
6
    (5)
 F = - 
253
672
    (6)

Multiply both sides of equation (4) by 10
Divide both sides of equation (4) by 19, get the equation：
        -2D = 
239
168
    (18)
, then add the two sides of equation (18) to both sides of equation (1), get the equation：
 A -3B = 
155
168
    (1)
 8B -4C = -1    (2)
 
5
2
C = - 
445
168
    (3)
- 
19
5
D = 
4541
1680
    (4)
 E = 
1
6
    (5)
 F = - 
253
672
    (6)

Multiply both sides of equation (3) by 8
Divide both sides of equation (3) by 5, get the equation：
         4C = - 
89
21
    (19)
, then add the two sides of equation (19) to both sides of equation (2), get the equation：
 A -3B = 
155
168
    (1)
 8B = - 
110
21
    (2)
 
5
2
C = - 
445
168
    (3)
 D = - 
239
336
    (4)
 E = 
1
6
    (5)
 F = - 
253
672
    (6)

Multiply both sides of equation (2) by 3
Divide both sides of equation (2) by 8, get the equation：
         3B = - 
55
28
    (20)
, then add the two sides of equation (20) to both sides of equation (1), get the equation：
 A = - 
25
24
    (1)
 8B = - 
110
21
    (2)
 C = - 
89
84
    (3)
 D = - 
239
336
    (4)
 E = 
1
6
    (5)
 F = - 
253
672
    (6)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = - 
25
24
    (1)
 B = - 
55
84
    (2)
 C = - 
89
84
    (3)
 D = - 
239
336
    (4)
 E = 
1
6
    (5)
 F = - 
253
672
    (6)


Therefore, the solution of the equation set is:
A = - 
25
24
B = - 
55
84
C = - 
89
84
D = - 
239
336
E = 
1
6
F = - 
253
672


Convert the solution of the equation set to decimals:
A = -1.041667
B = -0.654762
C = -1.059524
D = -0.711310
E = 0.166667
F = -0.376488

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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