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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 + 17C + 5D + E = 215    (1)
 A + B + 39C + 4D + 7E = 160    (2)
 5A + 22C + 3D + 4E = 217    (3)
 2A + 3B + 19C + 7D + 3E = 243    (4)
 6A + 24C + 4D + 5E = 242    (5)
Question solving process:

Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
 A + 17C + 5D + E = 215    (1)
 B + 22C -1D + 6E = -55    (2)
 5A + 22C + 3D + 4E = 217    (3)
 2A + 3B + 19C + 7D + 3E = 243    (4)
 6A + 24C + 4D + 5E = 242    (5)

Multiply both sides of equation (1) by 5, the equation can be obtained:
         5A + 85C + 25D + 5E = 1075    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 A + 17C + 5D + E = 215    (1)
 B + 22C -1D + 6E = -55    (2)
-63C -22D -1E = -858    (3)
 2A + 3B + 19C + 7D + 3E = 243    (4)
 6A + 24C + 4D + 5E = 242    (5)

Multiply both sides of equation (1) by 2, the equation can be obtained:
         2A + 34C + 10D + 2E = 430    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 A + 17C + 5D + E = 215    (1)
 B + 22C -1D + 6E = -55    (2)
-63C -22D -1E = -858    (3)
 3B -15C -3D + E = -187    (4)
 6A + 24C + 4D + 5E = 242    (5)

Multiply both sides of equation (1) by 6, the equation can be obtained:
         6A + 102C + 30D + 6E = 1290    (8)
, then subtract both sides of equation (8) from both sides of equation (5), the equations are reduced to:
 A + 17C + 5D + E = 215    (1)
 B + 22C -1D + 6E = -55    (2)
-63C -22D -1E = -858    (3)
 3B -15C -3D + E = -187    (4)
-78C -26D -1E = -1048    (5)

Multiply both sides of equation (2) by 3, the equation can be obtained:
         3B + 66C -3D + 18E = -165    (9)
, then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
 A + 17C + 5D + E = 215    (1)
 B + 22C -1D + 6E = -55    (2)
-63C -22D -1E = -858    (3)
-81C -17E = -22    (4)
-78C -26D -1E = -1048    (5)

Multiply both sides of equation (3) by 9
Divide the two sides of equation (3) by 7, the equation can be obtained:
        -81C - 
198
7
D - 
9
7
E = - 
7722
7
    (10)
, then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
 A + 17C + 5D + E = 215    (1)
 B + 22C -1D + 6E = -55    (2)
-63C -22D -1E = -858    (3)
 
198
7
D - 
110
7
E = 
7568
7
    (4)
-78C -26D -1E = -1048    (5)

Multiply both sides of equation (3) by 26
Divide the two sides of equation (3) by 21, the equation can be obtained:
        -78C - 
572
21
D - 
26
21
E = - 
7436
7
    (11)
, then subtract both sides of equation (11) from both sides of equation (5), the equations are reduced to:
 A + 17C + 5D + E = 215    (1)
 B + 22C -1D + 6E = -55    (2)
-63C -22D -1E = -858    (3)
 
198
7
D - 
110
7
E = 
7568
7
    (4)
 
26
21
D + 
5
21
E = 
100
7
    (5)

Multiply both sides of equation (4) by 13
Divide the two sides of equation (4) by 297, the equation can be obtained:
         
26
21
D - 
130
189
E = 
8944
189
    (12)
, then subtract both sides of equation (12) from both sides of equation (5), the equations are reduced to:
 A + 17C + 5D + E = 215    (1)
 B + 22C -1D + 6E = -55    (2)
-63C -22D -1E = -858    (3)
 
198
7
D - 
110
7
E = 
7568
7
    (4)
 
25
27
E = - 
892
27
    (5)

Multiply both sides of equation (5) by 594
Divide both sides of equation (5) by 35, get the equation：
         
110
7
E = - 
19624
35
    (13)
, then add the two sides of equation (13) to both sides of equation (4), get the equation：
 A + 17C + 5D + E = 215    (1)
 B + 22C -1D + 6E = -55    (2)
-63C -22D -1E = -858    (3)
 
198
7
D = 
18216
35
    (4)
 
25
27
E = - 
892
27
    (5)

Multiply both sides of equation (5) by 27
Divide both sides of equation (5) by 25, get the equation：
         E = - 
892
25
    (14)
, then add the two sides of equation (14) to both sides of equation (3), get the equation：
 A + 17C + 5D + E = 215    (1)
 B + 22C -1D + 6E = -55    (2)
-63C -22D = - 
22342
25
    (3)
 
198
7
D = 
18216
35
    (4)
 
25
27
E = - 
892
27
    (5)

Multiply both sides of equation (5) by 162
Divide both sides of equation (5) by 25, get the equation：
         6E = - 
5352
25
    (15)
, then subtract both sides of equation (15) from both sides of equation (2), get the equation：
 A + 17C + 5D + E = 215    (1)
 B + 22C -1D = 
3977
25
    (2)
-63C -22D = - 
22342
25
    (3)
 
198
7
D = 
18216
35
    (4)
 
25
27
E = - 
892
27
    (5)

Multiply both sides of equation (5) by 27
Divide both sides of equation (5) by 25, get the equation：
         E = - 
892
25
    (16)
, then subtract both sides of equation (16) from both sides of equation (1), get the equation：
 A + 17C + 5D = 
6267
25
    (1)
 B + 22C -1D = 
3977
25
    (2)
-63C -22D = - 
22342
25
    (3)
 
198
7
D = 
18216
35
    (4)
 
25
27
E = - 
892
27
    (5)

Multiply both sides of equation (4) by 7
Divide both sides of equation (4) by 9, get the equation：
         22D = 
2024
5
    (17)
, then add the two sides of equation (17) to both sides of equation (3), get the equation：
 A + 17C + 5D = 
6267
25
    (1)
 B + 22C -1D = 
3977
25
    (2)
-63C = - 
12222
25
    (3)
 
198
7
D = 
18216
35
    (4)
 E = - 
892
25
    (5)

Multiply both sides of equation (4) by 7
Divide both sides of equation (4) by 198, get the equation：
         D = 
92
5
    (18)
, then add the two sides of equation (18) to both sides of equation (2), get the equation：
 A + 17C + 5D = 
6267
25
    (1)
 B + 22C = 
4437
25
    (2)
-63C = - 
12222
25
    (3)
 
198
7
D = 
18216
35
    (4)
 E = - 
892
25
    (5)

Multiply both sides of equation (4) by 35
Divide both sides of equation (4) by 198, get the equation：
         5D = 92    (19)
, then subtract both sides of equation (19) from both sides of equation (1), get the equation：
 A + 17C = 
3967
25
    (1)
 B + 22C = 
4437
25
    (2)
-63C = - 
12222
25
    (3)
 
198
7
D = 
18216
35
    (4)
 E = - 
892
25
    (5)

Multiply both sides of equation (3) by 22
Divide both sides of equation (3) by 63, get the equation：
        -22C = - 
4268
25
    (20)
, then add the two sides of equation (20) to both sides of equation (2), get the equation：
 A + 17C = 
3967
25
    (1)
 B = 
169
25
    (2)
-63C = - 
12222
25
    (3)
 D = 
92
5
    (4)
 E = - 
892
25
    (5)

Multiply both sides of equation (3) by 17
Divide both sides of equation (3) by 63, get the equation：
        -17C = - 
3298
25
    (21)
, then add the two sides of equation (21) to both sides of equation (1), get the equation：
 A = 
669
25
    (1)
 B = 
169
25
    (2)
-63C = - 
12222
25
    (3)
 D = 
92
5
    (4)
 E = - 
892
25
    (5)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
669
25
    (1)
 B = 
169
25
    (2)
 C = 
194
25
    (3)
 D = 
92
5
    (4)
 E = - 
892
25
    (5)


Therefore, the solution of the equation set is:
A = 
669
25
B = 
169
25
C = 
194
25
D = 
92
5
E = - 
892
25


Convert the solution of the equation set to decimals:
A = 26.760000
B = 6.760000
C = 7.760000
D = 18.400000
E = -35.680000

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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