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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:
 6A + 14B -6C -2D = 0    (1)
-2A -3C + 5D = 30    (2)
-6B + 10C -3D = 0    (3)
 A -1B = -4    (4)
Question solving process:

Divide the two sides of equation (1) by 3, the equation can be obtained:
         2A + 
14
3
B -2C - 
2
3
D = 0    (5)
, then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
 6A + 14B -6C -2D = 0    (1)
 
14
3
B -5C + 
13
3
D = 30    (2)
-6B + 10C -3D = 0    (3)
 A -1B = -4    (4)

Divide the two sides of equation (1) by 6, the equation can be obtained:
         A + 
7
3
B -1C - 
1
3
D = 0    (6)
, then subtract both sides of equation (6) from both sides of equation (4), the equations are reduced to:
 6A + 14B -6C -2D = 0    (1)
 
14
3
B -5C + 
13
3
D = 30    (2)
-6B + 10C -3D = 0    (3)
- 
10
3
B + C + 
1
3
D = -4    (4)

Multiply both sides of equation (2) by 9
Divide the two sides of equation (2) by 7, the equation can be obtained:
         6B - 
45
7
C + 
39
7
D = 
270
7
    (7)
, then add the two sides of equation (7) to both sides of equation (3), the equations are reduced to:
 6A + 14B -6C -2D = 0    (1)
 
14
3
B -5C + 
13
3
D = 30    (2)
 
25
7
C + 
18
7
D = 
270
7
    (3)
- 
10
3
B + C + 
1
3
D = -4    (4)

Multiply both sides of equation (2) by 5
Divide the two sides of equation (2) by 7, the equation can be obtained:
         
10
3
B - 
25
7
C + 
65
21
D = 
150
7
    (8)
, then add the two sides of equation (8) to both sides of equation (4), the equations are reduced to:
 6A + 14B -6C -2D = 0    (1)
 
14
3
B -5C + 
13
3
D = 30    (2)
 
25
7
C + 
18
7
D = 
270
7
    (3)
- 
18
7
C + 
24
7
D = 
122
7
    (4)

Multiply both sides of equation (3) by 18
Divide the two sides of equation (3) by 25, the equation can be obtained:
         
18
7
C + 
324
175
D = 
972
35
    (9)
, then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
 6A + 14B -6C -2D = 0    (1)
 
14
3
B -5C + 
13
3
D = 30    (2)
 
25
7
C + 
18
7
D = 
270
7
    (3)
 
132
25
D = 
226
5
    (4)

Multiply both sides of equation (4) by 75
Divide both sides of equation (4) by 154, get the equation：
         
18
7
D = 
1695
77
    (10)
, then subtract both sides of equation (10) from both sides of equation (3), get the equation：
 6A + 14B -6C -2D = 0    (1)
 
14
3
B -5C + 
13
3
D = 30    (2)
 
25
7
C = 
1275
77
    (3)
 
132
25
D = 
226
5
    (4)

Multiply both sides of equation (4) by 325
Divide both sides of equation (4) by 396, get the equation：
         
13
3
D = 
7345
198
    (11)
, then subtract both sides of equation (11) from both sides of equation (2), get the equation：
 6A + 14B -6C -2D = 0    (1)
 
14
3
B -5C = - 
1405
198
    (2)
 
25
7
C = 
1275
77
    (3)
 
132
25
D = 
226
5
    (4)

Multiply both sides of equation (4) by 25
Divide both sides of equation (4) by 66, get the equation：
         2D = 
565
33
    (12)
, then add the two sides of equation (12) to both sides of equation (1), get the equation：
 6A + 14B -6C = 
565
33
    (1)
 
14
3
B -5C = - 
1405
198
    (2)
 
25
7
C = 
1275
77
    (3)
 
132
25
D = 
226
5
    (4)

Multiply both sides of equation (3) by 7
Divide both sides of equation (3) by 5, get the equation：
         5C = 
255
11
    (13)
, then add the two sides of equation (13) to both sides of equation (2), get the equation：
 6A + 14B -6C = 
565
33
    (1)
 
14
3
B = 
3185
198
    (2)
 
25
7
C = 
1275
77
    (3)
 D = 
565
66
    (4)

Multiply both sides of equation (3) by 42
Divide both sides of equation (3) by 25, get the equation：
         6C = 
306
11
    (14)
, then add the two sides of equation (14) to both sides of equation (1), get the equation：
 6A + 14B = 
1483
33
    (1)
 
14
3
B = 
3185
198
    (2)
 
25
7
C = 
1275
77
    (3)
 D = 
565
66
    (4)

Multiply both sides of equation (2) by 3, get the equation：
         14B = 
3185
66
    (15)
, then subtract both sides of equation (15) from both sides of equation (1), get the equation：
 6A = - 
73
22
    (1)
 
14
3
B = 
3185
198
    (2)
 C = 
51
11
    (3)
 D = 
565
66
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = - 
73
132
    (1)
 B = 
455
132
    (2)
 C = 
51
11
    (3)
 D = 
565
66
    (4)


Therefore, the solution of the equation set is:
A = - 
73
132
B = 
455
132
C = 
51
11
D = 
565
66


Convert the solution of the equation set to decimals:
A = -0.553030
B = 3.446970
C = 4.636364
D = 8.560606

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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