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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:
 11A -3B -2C -6D = -6    (1)
-3A + 4B -1C -3D = 0    (2)
-2A -1B + 5C -2D = 18    (3)
-6A -3B -2C + 11D = 0    (4)
Question solving process:

Multiply both sides of equation (1) by 3
Divide the two sides of equation (1) by 11, the equation can be obtained:
         3A - 
9
11
B - 
6
11
C - 
18
11
D = - 
18
11
    (5)
, then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
 11A -3B -2C -6D = -6    (1)
 
35
11
B - 
17
11
C - 
51
11
D = - 
18
11
    (2)
-2A -1B + 5C -2D = 18    (3)
-6A -3B -2C + 11D = 0    (4)

Multiply both sides of equation (1) by 2
Divide the two sides of equation (1) by 11, the equation can be obtained:
         2A - 
6
11
B - 
4
11
C - 
12
11
D = - 
12
11
    (6)
, then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
 11A -3B -2C -6D = -6    (1)
 
35
11
B - 
17
11
C - 
51
11
D = - 
18
11
    (2)
- 
17
11
B + 
51
11
C - 
34
11
D = 
186
11
    (3)
-6A -3B -2C + 11D = 0    (4)

Multiply both sides of equation (1) by 6
Divide the two sides of equation (1) by 11, the equation can be obtained:
         6A - 
18
11
B - 
12
11
C - 
36
11
D = - 
36
11
    (7)
, then add the two sides of equation (7) to both sides of equation (4), the equations are reduced to:
 11A -3B -2C -6D = -6    (1)
 
35
11
B - 
17
11
C - 
51
11
D = - 
18
11
    (2)
- 
17
11
B + 
51
11
C - 
34
11
D = 
186
11
    (3)
- 
51
11
B - 
34
11
C + 
85
11
D = - 
36
11
    (4)

Multiply both sides of equation (2) by 17
Divide the two sides of equation (2) by 35, the equation can be obtained:
         
17
11
B - 
289
385
C - 
867
385
D = - 
306
385
    (8)
, then add the two sides of equation (8) to both sides of equation (3), the equations are reduced to:
 11A -3B -2C -6D = -6    (1)
 
35
11
B - 
17
11
C - 
51
11
D = - 
18
11
    (2)
 
136
35
C - 
187
35
D = 
564
35
    (3)
- 
51
11
B - 
34
11
C + 
85
11
D = - 
36
11
    (4)

Multiply both sides of equation (2) by 51
Divide the two sides of equation (2) by 35, the equation can be obtained:
         
51
11
B - 
867
385
C - 
2601
385
D = - 
918
385
    (9)
, then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
 11A -3B -2C -6D = -6    (1)
 
35
11
B - 
17
11
C - 
51
11
D = - 
18
11
    (2)
 
136
35
C - 
187
35
D = 
564
35
    (3)
- 
187
35
C + 
34
35
D = - 
198
35
    (4)

Multiply both sides of equation (3) by 187
Divide the two sides of equation (3) by 136, the equation can be obtained:
         
187
35
C - 
2057
280
D = 
1551
70
    (10)
, then add the two sides of equation (10) to both sides of equation (4), the equations are reduced to:
 11A -3B -2C -6D = -6    (1)
 
35
11
B - 
17
11
C - 
51
11
D = - 
18
11
    (2)
 
136
35
C - 
187
35
D = 
564
35
    (3)
- 
51
8
D = 
33
2
    (4)

Multiply both sides of equation (4) by 88
Divide both sides of equation (4) by 105, get the equation：
        - 
187
35
D = 
484
35
    (11)
, then subtract both sides of equation (11) from both sides of equation (3), get the equation：
 11A -3B -2C -6D = -6    (1)
 
35
11
B - 
17
11
C - 
51
11
D = - 
18
11
    (2)
 
136
35
C = 
16
7
    (3)
- 
51
8
D = 
33
2
    (4)

Multiply both sides of equation (4) by 8
Divide both sides of equation (4) by 11, get the equation：
        - 
51
11
D = 12    (12)
, then subtract both sides of equation (12) from both sides of equation (2), get the equation：
 11A -3B -2C -6D = -6    (1)
 
35
11
B - 
17
11
C = - 
150
11
    (2)
 
136
35
C = 
16
7
    (3)
- 
51
8
D = 
33
2
    (4)

Multiply both sides of equation (4) by 16
Divide both sides of equation (4) by 17, get the equation：
        -6D = 
264
17
    (13)
, then subtract both sides of equation (13) from both sides of equation (1), get the equation：
 11A -3B -2C = - 
366
17
    (1)
 
35
11
B - 
17
11
C = - 
150
11
    (2)
 
136
35
C = 
16
7
    (3)
- 
51
8
D = 
33
2
    (4)

Multiply both sides of equation (3) by 35
Divide both sides of equation (3) by 88, get the equation：
         
17
11
C = 
10
11
    (14)
, then add the two sides of equation (14) to both sides of equation (2), get the equation：
 11A -3B -2C = - 
366
17
    (1)
 
35
11
B = - 
140
11
    (2)
 
136
35
C = 
16
7
    (3)
 D = - 
44
17
    (4)

Multiply both sides of equation (3) by 35
Divide both sides of equation (3) by 68, get the equation：
         2C = 
20
17
    (15)
, then add the two sides of equation (15) to both sides of equation (1), get the equation：
 11A -3B = - 
346
17
    (1)
 
35
11
B = - 
140
11
    (2)
 
136
35
C = 
16
7
    (3)
 D = - 
44
17
    (4)

Multiply both sides of equation (2) by 33
Divide both sides of equation (2) by 35, get the equation：
         3B = -12    (16)
, then add the two sides of equation (16) to both sides of equation (1), get the equation：
 11A = - 
550
17
    (1)
 
35
11
B = - 
140
11
    (2)
 C = 
10
17
    (3)
 D = - 
44
17
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = - 
50
17
    (1)
 B = -4    (2)
 C = 
10
17
    (3)
 D = - 
44
17
    (4)


Therefore, the solution of the equation set is:
A = - 
50
17
B = -4
C = 
10
17
D = - 
44
17


Convert the solution of the equation set to decimals:
A = -2.941176
B = -4
C = 0.588235
D = -2.588235

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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