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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:
 5A + 22C + 3D + 4E = 217    (1)
 2A + 3B + 19C + 7D + 3E = 243    (2)
 28C + 6D + 2E = 256    (3)
 6A + 24C + 4D + 5E = 242    (4)
 3A + 27C + 6D + 2E = 213    (5)
Question solving process:

Multiply both sides of equation (1) by 2
Divide the two sides of equation (1) by 5, the equation can be obtained:
         2A + 
44
5
C + 
6
5
D + 
8
5
E = 
434
5
    (6)
, then subtract both sides of equation (6) from both sides of equation (2), the equations are reduced to:
 5A + 22C + 3D + 4E = 217    (1)
 3B + 
51
5
C + 
29
5
D + 
7
5
E = 
781
5
    (2)
 28C + 6D + 2E = 256    (3)
 6A + 24C + 4D + 5E = 242    (4)
 3A + 27C + 6D + 2E = 213    (5)

Multiply both sides of equation (1) by 6
Divide the two sides of equation (1) by 5, the equation can be obtained:
         6A + 
132
5
C + 
18
5
D + 
24
5
E = 
1302
5
    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 5A + 22C + 3D + 4E = 217    (1)
 3B + 
51
5
C + 
29
5
D + 
7
5
E = 
781
5
    (2)
 28C + 6D + 2E = 256    (3)
- 
12
5
C + 
2
5
D + 
1
5
E = - 
92
5
    (4)
 3A + 27C + 6D + 2E = 213    (5)

Multiply both sides of equation (1) by 3
Divide the two sides of equation (1) by 5, the equation can be obtained:
         3A + 
66
5
C + 
9
5
D + 
12
5
E = 
651
5
    (8)
, then subtract both sides of equation (8) from both sides of equation (5), the equations are reduced to:
 5A + 22C + 3D + 4E = 217    (1)
 3B + 
51
5
C + 
29
5
D + 
7
5
E = 
781
5
    (2)
 28C + 6D + 2E = 256    (3)
- 
12
5
C + 
2
5
D + 
1
5
E = - 
92
5
    (4)
 
69
5
C + 
21
5
D - 
2
5
E = 
414
5
    (5)

Multiply both sides of equation (3) by 3
Divide the two sides of equation (3) by 35, the equation can be obtained:
         
12
5
C + 
18
35
D + 
6
35
E = 
768
35
    (9)
, then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
 5A + 22C + 3D + 4E = 217    (1)
 3B + 
51
5
C + 
29
5
D + 
7
5
E = 
781
5
    (2)
 28C + 6D + 2E = 256    (3)
 
32
35
D + 
13
35
E = 
124
35
    (4)
 
69
5
C + 
21
5
D - 
2
5
E = 
414
5
    (5)

Multiply both sides of equation (3) by 69
Divide the two sides of equation (3) by 140, the equation can be obtained:
         
69
5
C + 
207
70
D + 
69
70
E = 
4416
35
    (10)
, then subtract both sides of equation (10) from both sides of equation (5), the equations are reduced to:
 5A + 22C + 3D + 4E = 217    (1)
 3B + 
51
5
C + 
29
5
D + 
7
5
E = 
781
5
    (2)
 28C + 6D + 2E = 256    (3)
 
32
35
D + 
13
35
E = 
124
35
    (4)
 
87
70
D - 
97
70
E = - 
1518
35
    (5)

Multiply both sides of equation (4) by 87
Divide the two sides of equation (4) by 64, the equation can be obtained:
         
87
70
D + 
1131
2240
E = 
2697
560
    (11)
, then subtract both sides of equation (11) from both sides of equation (5), the equations are reduced to:
 5A + 22C + 3D + 4E = 217    (1)
 3B + 
51
5
C + 
29
5
D + 
7
5
E = 
781
5
    (2)
 28C + 6D + 2E = 256    (3)
 
32
35
D + 
13
35
E = 
124
35
    (4)
- 
121
64
E = - 
771
16
    (5)

Multiply both sides of equation (5) by 832
Divide both sides of equation (5) by 4235, get the equation：
        - 
13
35
E = - 
40092
4235
    (12)
, then add the two sides of equation (12) to both sides of equation (4), get the equation：
 5A + 22C + 3D + 4E = 217    (1)
 3B + 
51
5
C + 
29
5
D + 
7
5
E = 
781
5
    (2)
 28C + 6D + 2E = 256    (3)
 
32
35
D = - 
3584
605
    (4)
- 
121
64
E = - 
771
16
    (5)

Multiply both sides of equation (5) by 128
Divide both sides of equation (5) by 121, get the equation：
        -2E = - 
6168
121
    (13)
, then add the two sides of equation (13) to both sides of equation (3), get the equation：
 5A + 22C + 3D + 4E = 217    (1)
 3B + 
51
5
C + 
29
5
D + 
7
5
E = 
781
5
    (2)
 28C + 6D = 
24808
121
    (3)
 
32
35
D = - 
3584
605
    (4)
- 
121
64
E = - 
771
16
    (5)

Multiply both sides of equation (5) by 448
Divide both sides of equation (5) by 605, get the equation：
        - 
7
5
E = - 
21588
605
    (14)
, then add the two sides of equation (14) to both sides of equation (2), get the equation：
 5A + 22C + 3D + 4E = 217    (1)
 3B + 
51
5
C + 
29
5
D = 
72913
605
    (2)
 28C + 6D = 
24808
121
    (3)
 
32
35
D = - 
3584
605
    (4)
- 
121
64
E = - 
771
16
    (5)

Multiply both sides of equation (5) by 256
Divide both sides of equation (5) by 121, get the equation：
        -4E = - 
12336
121
    (15)
, then add the two sides of equation (15) to both sides of equation (1), get the equation：
 5A + 22C + 3D = 
13921
121
    (1)
 3B + 
51
5
C + 
29
5
D = 
72913
605
    (2)
 28C + 6D = 
24808
121
    (3)
 
32
35
D = - 
3584
605
    (4)
- 
121
64
E = - 
771
16
    (5)

Multiply both sides of equation (4) by 105
Divide both sides of equation (4) by 16, get the equation：
         6D = - 
4704
121
    (16)
, then subtract both sides of equation (16) from both sides of equation (3), get the equation：
 5A + 22C + 3D = 
13921
121
    (1)
 3B + 
51
5
C + 
29
5
D = 
72913
605
    (2)
 28C = 
29512
121
    (3)
 
32
35
D = - 
3584
605
    (4)
 E = 
3084
121
    (5)

Multiply both sides of equation (4) by 203
Divide both sides of equation (4) by 32, get the equation：
         
29
5
D = - 
22736
605
    (17)
, then subtract both sides of equation (17) from both sides of equation (2), get the equation：
 5A + 22C + 3D = 
13921
121
    (1)
 3B + 
51
5
C = 
95649
605
    (2)
 28C = 
29512
121
    (3)
 
32
35
D = - 
3584
605
    (4)
 E = 
3084
121
    (5)

Multiply both sides of equation (4) by 105
Divide both sides of equation (4) by 32, get the equation：
         3D = - 
2352
121
    (18)
, then subtract both sides of equation (18) from both sides of equation (1), get the equation：
 5A + 22C = 
16273
121
    (1)
 3B + 
51
5
C = 
95649
605
    (2)
 28C = 
29512
121
    (3)
 
32
35
D = - 
3584
605
    (4)
 E = 
3084
121
    (5)

Multiply both sides of equation (3) by 51
Divide both sides of equation (3) by 140, get the equation：
         
51
5
C = 
53754
605
    (19)
, then subtract both sides of equation (19) from both sides of equation (2), get the equation：
 5A + 22C = 
16273
121
    (1)
 3B = 
8379
121
    (2)
 28C = 
29512
121
    (3)
 D = - 
784
121
    (4)
 E = 
3084
121
    (5)

Multiply both sides of equation (3) by 11
Divide both sides of equation (3) by 14, get the equation：
         22C = 
2108
11
    (20)
, then subtract both sides of equation (20) from both sides of equation (1), get the equation：
 5A = - 
6915
121
    (1)
 3B = 
8379
121
    (2)
 28C = 
29512
121
    (3)
 D = - 
784
121
    (4)
 E = 
3084
121
    (5)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = - 
1383
121
    (1)
 B = 
2793
121
    (2)
 C = 
1054
121
    (3)
 D = - 
784
121
    (4)
 E = 
3084
121
    (5)


Therefore, the solution of the equation set is:
A = - 
1383
121
B = 
2793
121
C = 
1054
121
D = - 
784
121
E = 
3084
121


Convert the solution of the equation set to decimals:
A = -11.429752
B = 23.082645
C = 8.710744
D = -6.479339
E = 25.487603

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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