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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)
0 = 0    (3)
 A + 6B + 3C + 67E = 38    (4)
 3A + 11B + C + 92E = 78    (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)
0 = 0    (3)
 A + 6B + 3C + 67E = 38    (4)
 3A + 11B + C + 92E = 78    (5)

Divide the two sides of equation (1) by 2, the equation can be obtained:
         A + 7B + 
1
2
C + 
93
2
E = 39    (6)
, then subtract both sides of equation (6) from both sides of equation (4), the equations are reduced to:
 2A + 14B + C + 93E = 78    (1)
 B + C + D -5E = -1    (2)
0 = 0    (3)
-1B + 
5
2
C + 
41
2
E = -1    (4)
 3A + 11B + C + 92E = 78    (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 (5), the equations are reduced to:
 2A + 14B + C + 93E = 78    (1)
 B + C + D -5E = -1    (2)
0 = 0    (3)
-1B + 
5
2
C + 
41
2
E = -1    (4)
-10B - 
1
2
C - 
95
2
E = -39    (5)

Add both sides of equation (2) to both sides of equation (4) ,the equations are reduced to:
 2A + 14B + C + 93E = 78    (1)
 B + C + D -5E = -1    (2)
0 = 0    (3)
 
7
2
C + D + 
31
2
E = -2    (4)
-10B - 
1
2
C - 
95
2
E = -39    (5)

Multiply both sides of equation (2) by 10, the equation can be obtained:
         10B + 10C + 10D -50E = -10    (8)
, then add the two sides of equation (8) to both sides of equation (5), the equations are reduced to:
 2A + 14B + C + 93E = 78    (1)
 B + C + D -5E = -1    (2)
0 = 0    (3)
 
7
2
C + D + 
31
2
E = -2    (4)
 
19
2
C + 10D - 
195
2
E = -49    (5)

交After the exchange of equation (3) and equation (4)， the equation system becomes:
 2A + 14B + C + 93E = 78    (1)
 B + C + D -5E = -1    (2)
 
7
2
C + D + 
31
2
E = -2    (3)
0 = 0    (4)
 
19
2
C + 10D - 
195
2
E = -49    (5)

Multiply both sides of equation (3) by 19
Divide the two sides of equation (3) by 7, the equation can be obtained:
         
19
2
C + 
19
7
D + 
589
14
E = - 
38
7
    (9)
, then subtract both sides of equation (9) from both sides of equation (5), the equations are reduced to:
 2A + 14B + C + 93E = 78    (1)
 B + C + D -5E = -1    (2)
 
7
2
C + D + 
31
2
E = -2    (3)
0 = 0    (4)
 
51
7
D - 
977
7
E = - 
305
7
    (5)

交After the exchange of equation (4) and equation (5)， the equation system becomes:
 2A + 14B + C + 93E = 78    (1)
 B + C + D -5E = -1    (2)
 
7
2
C + D + 
31
2
E = -2    (3)
 
51
7
D - 
977
7
E = - 
305
7
    (4)
0 = 0    (5)

Multiply both sides of equation (4) by 7
Divide both sides of equation (4) by 51, get the equation：
         D - 
977
51
E = - 
305
51
    (10)
, then subtract both sides of equation (10) from both sides of equation (3), get the equation：
 2A + 14B + C + 93E = 78    (1)
 B + C + D -5E = -1    (2)
 
7
2
C + 
3535
102
E = 
203
51
    (3)
 
51
7
D - 
977
7
E = - 
305
7
    (4)
0 = 0    (5)

Multiply both sides of equation (4) by 7
Divide both sides of equation (4) by 51, get the equation：
         D - 
977
51
E = - 
305
51
    (11)
, then subtract both sides of equation (11) from both sides of equation (2), get the equation：
 2A + 14B + C + 93E = 78    (1)
 B + C + 
722
51
E = 
254
51
    (2)
 
7
2
C + 
3535
102
E = 
203
51
    (3)
 
51
7
D - 
977
7
E = - 
305
7
    (4)
0 = 0    (5)

Multiply both sides of equation (3) by 2
Divide both sides of equation (3) by 7, get the equation：
         C + 
505
51
E = 
58
51
    (12)
, then subtract both sides of equation (12) from both sides of equation (2), get the equation：
 2A + 14B + C + 93E = 78    (1)
 B + 
217
51
E = 
196
51
    (2)
 
7
2
C + 
3535
102
E = 
203
51
    (3)
 D - 
977
51
E = - 
305
51
    (4)
0 = 0    (5)

Multiply both sides of equation (3) by 2
Divide both sides of equation (3) by 7, get the equation：
         C + 
505
51
E = 
58
51
    (13)
, then subtract both sides of equation (13) from both sides of equation (1), get the equation：
 2A + 14B + 
4238
51
E = 
3920
51
    (1)
 B + 
217
51
E = 
196
51
    (2)
 
7
2
C + 
3535
102
E = 
203
51
    (3)
 D - 
977
51
E = - 
305
51
    (4)
0 = 0    (5)

Multiply both sides of equation (2) by 14, get the equation：
         14B + 
3038
51
E = 
2744
51
    (14)
, then subtract both sides of equation (14) from both sides of equation (1), get the equation：
 2A + 
400
17
E = 
392
17
    (1)
 B + 
217
51
E = 
196
51
    (2)
 C + 
505
51
E = 
58
51
    (3)
 D - 
977
51
E = - 
305
51
    (4)
0 = 0    (5)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A + 
200
17
E = 
196
17
    (1)
 B + 
217
51
E = 
196
51
    (2)
 C + 
505
51
E = 
58
51
    (3)
 D - 
977
51
E = - 
305
51
    (4)
0 = 0    (5)


Therefore, the solution of the equation set is:
A = 
196
17
 - 
200
17
E
B = 
196
51
 - 
217
51
E
C = 
58
51
 - 
505
51
E
D = - 
305
51
 + 
977
51
E


Convert the solution of the equation set to decimals:
A = 11.529412 - 
200
17
E
B = 3.843137 - 
217
51
E
C = 1.137255 - 
505
51
E
D = -5.980392 + 
977
51
E

Where:  E are arbitrary constants.
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