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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:
 2A + 14B + C + 93E = 78    (1)
 2A + 15B + 2C + D + 88E = 77    (2)
 14A + 31B + 4C + 2D + 89E = 195    (3)
 3A + 17B + 5C + 6D + 77E = 83    (4)
 8A + 24B + C + 4D + 96E = 131    (5)
Question solving process:

Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
 2A + 14B + C + 93E = 78    (1)
 B + C + D -5E = -1    (2)
 14A + 31B + 4C + 2D + 89E = 195    (3)
 3A + 17B + 5C + 6D + 77E = 83    (4)
 8A + 24B + C + 4D + 96E = 131    (5)

Multiply both sides of equation (1) by 7, the equation can be obtained:
         14A + 98B + 7C + 651E = 546    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 2A + 14B + C + 93E = 78    (1)
 B + C + D -5E = -1    (2)
-67B -3C + 2D -562E = -351    (3)
 3A + 17B + 5C + 6D + 77E = 83    (4)
 8A + 24B + C + 4D + 96E = 131    (5)

Multiply both sides of equation (1) by 3
Divide the two sides of equation (1) by 2, the equation can be obtained:
         3A + 21B + 
3
2
C + 
279
2
E = 117    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 2A + 14B + C + 93E = 78    (1)
 B + C + D -5E = -1    (2)
-67B -3C + 2D -562E = -351    (3)
-4B + 
7
2
C + 6D - 
125
2
E = -34    (4)
 8A + 24B + C + 4D + 96E = 131    (5)

Multiply both sides of equation (1) by 4, the equation can be obtained:
         8A + 56B + 4C + 372E = 312    (8)
, then subtract both sides of equation (8) from both sides of equation (5), the equations are reduced to:
 2A + 14B + C + 93E = 78    (1)
 B + C + D -5E = -1    (2)
-67B -3C + 2D -562E = -351    (3)
-4B + 
7
2
C + 6D - 
125
2
E = -34    (4)
-32B -3C + 4D -276E = -181    (5)

Multiply both sides of equation (2) by 67, the equation can be obtained:
         67B + 67C + 67D -335E = -67    (9)
, then add the two sides of equation (9) to both sides of equation (3), the equations are reduced to:
 2A + 14B + C + 93E = 78    (1)
 B + C + D -5E = -1    (2)
 64C + 69D -897E = -418    (3)
-4B + 
7
2
C + 6D - 
125
2
E = -34    (4)
-32B -3C + 4D -276E = -181    (5)

Multiply both sides of equation (2) by 4, the equation can be obtained:
         4B + 4C + 4D -20E = -4    (10)
, then add the two sides of equation (10) to both sides of equation (4), the equations are reduced to:
 2A + 14B + C + 93E = 78    (1)
 B + C + D -5E = -1    (2)
 64C + 69D -897E = -418    (3)
 
15
2
C + 10D - 
165
2
E = -38    (4)
-32B -3C + 4D -276E = -181    (5)

Multiply both sides of equation (2) by 32, the equation can be obtained:
         32B + 32C + 32D -160E = -32    (11)
, then add the two sides of equation (11) to both sides of equation (5), the equations are reduced to:
 2A + 14B + C + 93E = 78    (1)
 B + C + D -5E = -1    (2)
 64C + 69D -897E = -418    (3)
 
15
2
C + 10D - 
165
2
E = -38    (4)
 29C + 36D -436E = -213    (5)

Multiply both sides of equation (3) by 15
Divide the two sides of equation (3) by 128, the equation can be obtained:
         
15
2
C + 
1035
128
D - 
13455
128
E = - 
3135
64
    (12)
, then subtract both sides of equation (12) from both sides of equation (4), the equations are reduced to:
 2A + 14B + C + 93E = 78    (1)
 B + C + D -5E = -1    (2)
 64C + 69D -897E = -418    (3)
 
245
128
D + 
2895
128
E = 
703
64
    (4)
 29C + 36D -436E = -213    (5)

Multiply both sides of equation (3) by 29
Divide the two sides of equation (3) by 64, the equation can be obtained:
         29C + 
2001
64
D - 
26013
64
E = - 
6061
32
    (13)
, then subtract both sides of equation (13) from both sides of equation (5), the equations are reduced to:
 2A + 14B + C + 93E = 78    (1)
 B + C + D -5E = -1    (2)
 64C + 69D -897E = -418    (3)
 
245
128
D + 
2895
128
E = 
703
64
    (4)
 
303
64
D - 
1891
64
E = - 
755
32
    (5)

Multiply both sides of equation (4) by 606
Divide the two sides of equation (4) by 245, the equation can be obtained:
         
303
64
D + 
175437
3136
E = 
213009
7840
    (14)
, then subtract both sides of equation (14) from both sides of equation (5), the equations are reduced to:
 2A + 14B + C + 93E = 78    (1)
 B + C + D -5E = -1    (2)
 64C + 69D -897E = -418    (3)
 
245
128
D + 
2895
128
E = 
703
64
    (4)
- 
4189
49
E = - 
12437
245
    (5)

Multiply both sides of equation (5) by 141855
Divide both sides of equation (5) by 536192, get the equation：
        - 
2895
128
E = - 
7201023
536192
    (15)
, then add the two sides of equation (15) to both sides of equation (4), get the equation：
 2A + 14B + C + 93E = 78    (1)
 B + C + D -5E = -1    (2)
 64C + 69D -897E = -418    (3)
 
245
128
D = - 
1311289
536192
    (4)
- 
4189
49
E = - 
12437
245
    (5)

Multiply both sides of equation (5) by 43953
Divide both sides of equation (5) by 4189, get the equation：
        -897E = - 
11155989
20945
    (16)
, then subtract both sides of equation (16) from both sides of equation (3), get the equation：
 2A + 14B + C + 93E = 78    (1)
 B + C + D -5E = -1    (2)
 64C + 69D = 
2400979
20945
    (3)
 
245
128
D = - 
1311289
536192
    (4)
- 
4189
49
E = - 
12437
245
    (5)

Multiply both sides of equation (5) by 245
Divide both sides of equation (5) by 4189, get the equation：
        -5E = - 
12437
4189
    (17)
, then subtract both sides of equation (17) from both sides of equation (2), get the equation：
 2A + 14B + C + 93E = 78    (1)
 B + C + D = 
8248
4189
    (2)
 64C + 69D = 
2400979
20945
    (3)
 
245
128
D = - 
1311289
536192
    (4)
- 
4189
49
E = - 
12437
245
    (5)

Multiply both sides of equation (5) by 4557
Divide both sides of equation (5) by 4189, get the equation：
        -93E = - 
1156641
20945
    (18)
, then add the two sides of equation (18) to both sides of equation (1), get the equation：
 2A + 14B + C = 
477069
20945
    (1)
 B + C + D = 
8248
4189
    (2)
 64C + 69D = 
2400979
20945
    (3)
 
245
128
D = - 
1311289
536192
    (4)
- 
4189
49
E = - 
12437
245
    (5)

Multiply both sides of equation (4) by 8832
Divide both sides of equation (4) by 245, get the equation：
         69D = - 
1846509
20945
    (19)
, then subtract both sides of equation (19) from both sides of equation (3), get the equation：
 2A + 14B + C = 
477069
20945
    (1)
 B + C + D = 
8248
4189
    (2)
 64C = 
4247488
20945
    (3)
 
245
128
D = - 
1311289
536192
    (4)
 E = 
12437
20945
    (5)

Multiply both sides of equation (4) by 128
Divide both sides of equation (4) by 245, get the equation：
         D = - 
26761
20945
    (20)
, then subtract both sides of equation (20) from both sides of equation (2), get the equation：
 2A + 14B + C = 
477069
20945
    (1)
 B + C = 
68001
20945
    (2)
 64C = 
4247488
20945
    (3)
 
245
128
D = - 
1311289
536192
    (4)
 E = 
12437
20945
    (5)

Divide both sides of equation (3) by 64, get the equation：
         C = 
66367
20945
    (21)
, then subtract both sides of equation (21) from both sides of equation (2), get the equation：
 2A + 14B + C = 
477069
20945
    (1)
 B = 
1634
20945
    (2)
 64C = 
4247488
20945
    (3)
 D = - 
26761
20945
    (4)
 E = 
12437
20945
    (5)

Divide both sides of equation (3) by 64, get the equation：
         C = 
66367
20945
    (22)
, then subtract both sides of equation (22) from both sides of equation (1), get the equation：
 2A + 14B = 
410702
20945
    (1)
 B = 
1634
20945
    (2)
 64C = 
4247488
20945
    (3)
 D = - 
26761
20945
    (4)
 E = 
12437
20945
    (5)

Multiply both sides of equation (2) by 14, get the equation：
         14B = 
22876
20945
    (23)
, then subtract both sides of equation (23) from both sides of equation (1), get the equation：
 2A = 
387826
20945
    (1)
 B = 
1634
20945
    (2)
 C = 
66367
20945
    (3)
 D = - 
26761
20945
    (4)
 E = 
12437
20945
    (5)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
193913
20945
    (1)
 B = 
1634
20945
    (2)
 C = 
66367
20945
    (3)
 D = - 
26761
20945
    (4)
 E = 
12437
20945
    (5)


Therefore, the solution of the equation set is:
A = 
193913
20945
B = 
1634
20945
C = 
66367
20945
D = - 
26761
20945
E = 
12437
20945


Convert the solution of the equation set to decimals:
A = 9.258200
B = 0.078014
C = 3.168632
D = -1.277680
E = 0.593793

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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