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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:
 12A -8B -4D = 17    (1)
-8A + 28B -12C = 0    (2)
-12B + 36C -12D -12E = 0    (3)
-4A -12C + 20D -4E = 0    (4)
-12C -4D + 20E = 0    (5)
Question solving process:

Multiply both sides of equation (1) by 2
Divide the two sides of equation (1) by 3, the equation can be obtained:
         8A - 
16
3
B - 
8
3
D = 
34
3
    (6)
, then add the two sides of equation (6) to both sides of equation (2), the equations are reduced to:
 12A -8B -4D = 17    (1)
 
68
3
B -12C - 
8
3
D = 
34
3
    (2)
-12B + 36C -12D -12E = 0    (3)
-4A -12C + 20D -4E = 0    (4)
-12C -4D + 20E = 0    (5)

Divide the two sides of equation (1) by 3, the equation can be obtained:
         4A - 
8
3
B - 
4
3
D = 
17
3
    (7)
, then add the two sides of equation (7) to both sides of equation (4), the equations are reduced to:
 12A -8B -4D = 17    (1)
 
68
3
B -12C - 
8
3
D = 
34
3
    (2)
-12B + 36C -12D -12E = 0    (3)
- 
8
3
B -12C + 
56
3
D -4E = 
17
3
    (4)
-12C -4D + 20E = 0    (5)

Multiply both sides of equation (2) by 9
Divide the two sides of equation (2) by 17, the equation can be obtained:
         12B - 
108
17
C - 
24
17
D = 6    (8)
, then add the two sides of equation (8) to both sides of equation (3), the equations are reduced to:
 12A -8B -4D = 17    (1)
 
68
3
B -12C - 
8
3
D = 
34
3
    (2)
 
504
17
C - 
228
17
D -12E = 6    (3)
- 
8
3
B -12C + 
56
3
D -4E = 
17
3
    (4)
-12C -4D + 20E = 0    (5)

Multiply both sides of equation (2) by 2
Divide the two sides of equation (2) by 17, the equation can be obtained:
         
8
3
B - 
24
17
C - 
16
51
D = 
4
3
    (9)
, then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
 12A -8B -4D = 17    (1)
 
68
3
B -12C - 
8
3
D = 
34
3
    (2)
 
504
17
C - 
228
17
D -12E = 6    (3)
- 
228
17
C + 
312
17
D -4E = 7    (4)
-12C -4D + 20E = 0    (5)

Multiply both sides of equation (3) by 19
Divide the two sides of equation (3) by 42, the equation can be obtained:
         
228
17
C - 
722
119
D - 
38
7
E = 
19
7
    (10)
, then add the two sides of equation (10) to both sides of equation (4), the equations are reduced to:
 12A -8B -4D = 17    (1)
 
68
3
B -12C - 
8
3
D = 
34
3
    (2)
 
504
17
C - 
228
17
D -12E = 6    (3)
 
1462
119
D - 
66
7
E = 
68
7
    (4)
-12C -4D + 20E = 0    (5)

Multiply both sides of equation (3) by 17
Divide the two sides of equation (3) by 42, the equation can be obtained:
         12C - 
38
7
D - 
34
7
E = 
17
7
    (11)
, then add the two sides of equation (11) to both sides of equation (5), the equations are reduced to:
 12A -8B -4D = 17    (1)
 
68
3
B -12C - 
8
3
D = 
34
3
    (2)
 
504
17
C - 
228
17
D -12E = 6    (3)
 
1462
119
D - 
66
7
E = 
68
7
    (4)
- 
66
7
D + 
106
7
E = 
17
7
    (5)

Multiply both sides of equation (4) by 561
Divide the two sides of equation (4) by 731, the equation can be obtained:
         
1122
119
D - 
2178
301
E = 
2244
301
    (12)
, then add the two sides of equation (12) to both sides of equation (5), the equations are reduced to:
 12A -8B -4D = 17    (1)
 
68
3
B -12C - 
8
3
D = 
34
3
    (2)
 
504
17
C - 
228
17
D -12E = 6    (3)
 
1462
119
D - 
66
7
E = 
68
7
    (4)
 
340
43
E = 
425
43
    (5)

Multiply both sides of equation (5) by 1419
Divide both sides of equation (5) by 1190, get the equation：
         
66
7
E = 
165
14
    (13)
, then add the two sides of equation (13) to both sides of equation (4), get the equation：
 12A -8B -4D = 17    (1)
 
68
3
B -12C - 
8
3
D = 
34
3
    (2)
 
504
17
C - 
228
17
D -12E = 6    (3)
 
1462
119
D = 
43
2
    (4)
 
340
43
E = 
425
43
    (5)

Multiply both sides of equation (5) by 129
Divide both sides of equation (5) by 85, get the equation：
         12E = 15    (14)
, then add the two sides of equation (14) to both sides of equation (3), get the equation：
 12A -8B -4D = 17    (1)
 
68
3
B -12C - 
8
3
D = 
34
3
    (2)
 
504
17
C - 
228
17
D = 21    (3)
 
1462
119
D = 
43
2
    (4)
 
340
43
E = 
425
43
    (5)

Multiply both sides of equation (4) by 798
Divide both sides of equation (4) by 731, get the equation：
         
228
17
D = 
399
17
    (15)
, then add the two sides of equation (15) to both sides of equation (3), get the equation：
 12A -8B -4D = 17    (1)
 
68
3
B -12C - 
8
3
D = 
34
3
    (2)
 
504
17
C = 
756
17
    (3)
 
1462
119
D = 
43
2
    (4)
 E = 
5
4
    (5)

Multiply both sides of equation (4) by 476
Divide both sides of equation (4) by 2193, get the equation：
         
8
3
D = 
14
3
    (16)
, then add the two sides of equation (16) to both sides of equation (2), get the equation：
 12A -8B -4D = 17    (1)
 
68
3
B -12C = 16    (2)
 
504
17
C = 
756
17
    (3)
 
1462
119
D = 
43
2
    (4)
 E = 
5
4
    (5)

Multiply both sides of equation (4) by 238
Divide both sides of equation (4) by 731, get the equation：
         4D = 7    (17)
, then add the two sides of equation (17) to both sides of equation (1), get the equation：
 12A -8B = 24    (1)
 
68
3
B -12C = 16    (2)
 
504
17
C = 
756
17
    (3)
 
1462
119
D = 
43
2
    (4)
 E = 
5
4
    (5)

Multiply both sides of equation (3) by 17
Divide both sides of equation (3) by 42, get the equation：
         12C = 18    (18)
, then add the two sides of equation (18) to both sides of equation (2), get the equation：
 12A -8B = 24    (1)
 
68
3
B = 34    (2)
 
504
17
C = 
756
17
    (3)
 D = 
7
4
    (4)
 E = 
5
4
    (5)

Multiply both sides of equation (2) by 6
Divide both sides of equation (2) by 17, get the equation：
         8B = 12    (19)
, then add the two sides of equation (19) to both sides of equation (1), get the equation：
 12A = 36    (1)
 
68
3
B = 34    (2)
 C = 
3
2
    (3)
 D = 
7
4
    (4)
 E = 
5
4
    (5)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 3    (1)
 B = 
3
2
    (2)
 C = 
3
2
    (3)
 D = 
7
4
    (4)
 E = 
5
4
    (5)


Therefore, the solution of the equation set is:
A = 3
B = 
3
2
C = 
3
2
D = 
7
4
E = 
5
4


Convert the solution of the equation set to decimals:
A = 3
B = 1.500000
C = 1.500000
D = 1.750000
E = 1.250000

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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