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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:
 4A + 2B + 3C + 4D + 5E = 9    (1)
 5A -2B + 3C -6D + 5E = 7    (2)
 2A + 3B + 7C + 2D + 3E = 8    (3)
 7A + 5B + 6C + 9D + 8E = 3    (4)
0 = 0    (5)
Question solving process:

Multiply both sides of equation (1) by 5
Divide the two sides of equation (1) by 4, the equation can be obtained:
         5A + 
5
2
B + 
15
4
C + 5D + 
25
4
E = 
45
4
    (6)
, then subtract both sides of equation (6) from both sides of equation (2), the equations are reduced to:
 4A + 2B + 3C + 4D + 5E = 9    (1)
- 
9
2
B - 
3
4
C -11D - 
5
4
E = - 
17
4
    (2)
 2A + 3B + 7C + 2D + 3E = 8    (3)
 7A + 5B + 6C + 9D + 8E = 3    (4)
0 = 0    (5)

Divide the two sides of equation (1) by 2, the equation can be obtained:
         2A + B + 
3
2
C + 2D + 
5
2
E = 
9
2
    (7)
, then subtract both sides of equation (7) from both sides of equation (3), the equations are reduced to:
 4A + 2B + 3C + 4D + 5E = 9    (1)
- 
9
2
B - 
3
4
C -11D - 
5
4
E = - 
17
4
    (2)
 2B + 
11
2
C + 
1
2
E = 
7
2
    (3)
 7A + 5B + 6C + 9D + 8E = 3    (4)
0 = 0    (5)

Multiply both sides of equation (1) by 7
Divide the two sides of equation (1) by 4, the equation can be obtained:
         7A + 
7
2
B + 
21
4
C + 7D + 
35
4
E = 
63
4
    (8)
, then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
 4A + 2B + 3C + 4D + 5E = 9    (1)
- 
9
2
B - 
3
4
C -11D - 
5
4
E = - 
17
4
    (2)
 2B + 
11
2
C + 
1
2
E = 
7
2
    (3)
 
3
2
B + 
3
4
C + 2D - 
3
4
E = - 
51
4
    (4)
0 = 0    (5)

Multiply both sides of equation (2) by 4
Divide the two sides of equation (2) by 9, the equation can be obtained:
        -2B - 
1
3
C - 
44
9
D - 
5
9
E = - 
17
9
    (9)
, then add the two sides of equation (9) to both sides of equation (3), the equations are reduced to:
 4A + 2B + 3C + 4D + 5E = 9    (1)
- 
9
2
B - 
3
4
C -11D - 
5
4
E = - 
17
4
    (2)
 
31
6
C - 
44
9
D - 
1
18
E = 
29
18
    (3)
 
3
2
B + 
3
4
C + 2D - 
3
4
E = - 
51
4
    (4)
0 = 0    (5)

Divide the two sides of equation (2) by 3, the equation can be obtained:
        - 
3
2
B - 
1
4
C - 
11
3
D - 
5
12
E = - 
17
12
    (10)
, then add the two sides of equation (10) to both sides of equation (4), the equations are reduced to:
 4A + 2B + 3C + 4D + 5E = 9    (1)
- 
9
2
B - 
3
4
C -11D - 
5
4
E = - 
17
4
    (2)
 
31
6
C - 
44
9
D - 
1
18
E = 
29
18
    (3)
 
1
2
C - 
5
3
D - 
7
6
E = - 
85
6
    (4)
0 = 0    (5)

Multiply both sides of equation (3) by 3
Divide the two sides of equation (3) by 31, the equation can be obtained:
         
1
2
C - 
44
93
D - 
1
186
E = 
29
186
    (11)
, then subtract both sides of equation (11) from both sides of equation (4), the equations are reduced to:
 4A + 2B + 3C + 4D + 5E = 9    (1)
- 
9
2
B - 
3
4
C -11D - 
5
4
E = - 
17
4
    (2)
 
31
6
C - 
44
9
D - 
1
18
E = 
29
18
    (3)
- 
37
31
D - 
36
31
E = - 
444
31
    (4)
0 = 0    (5)

Multiply both sides of equation (4) by 1364
Divide both sides of equation (4) by 333, get the equation：
        - 
44
9
D - 
176
37
E = - 
6512
111
    (12)
, then subtract both sides of equation (12) from both sides of equation (3), get the equation：
 4A + 2B + 3C + 4D + 5E = 9    (1)
- 
9
2
B - 
3
4
C -11D - 
5
4
E = - 
17
4
    (2)
 
31
6
C + 
3131
666
E = 
40145
666
    (3)
- 
37
31
D - 
36
31
E = - 
444
31
    (4)
0 = 0    (5)

Multiply both sides of equation (4) by 341
Divide both sides of equation (4) by 37, get the equation：
        -11D - 
396
37
E = -132    (13)
, then subtract both sides of equation (13) from both sides of equation (2), get the equation：
 4A + 2B + 3C + 4D + 5E = 9    (1)
- 
9
2
B - 
3
4
C + 
1399
148
E = 
511
4
    (2)
 
31
6
C + 
3131
666
E = 
40145
666
    (3)
- 
37
31
D - 
36
31
E = - 
444
31
    (4)
0 = 0    (5)

Multiply both sides of equation (4) by 124
Divide both sides of equation (4) by 37, get the equation：
        -4D - 
144
37
E = -48    (14)
, then add the two sides of equation (14) to both sides of equation (1), get the equation：
 4A + 2B + 3C + 
41
37
E = -39    (1)
- 
9
2
B - 
3
4
C + 
1399
148
E = 
511
4
    (2)
 
31
6
C + 
3131
666
E = 
40145
666
    (3)
- 
37
31
D - 
36
31
E = - 
444
31
    (4)
0 = 0    (5)

Multiply both sides of equation (3) by 9
Divide both sides of equation (3) by 62, get the equation：
         
3
4
C + 
101
148
E = 
1295
148
    (15)
, then add the two sides of equation (15) to both sides of equation (2), get the equation：
 4A + 2B + 3C + 
41
37
E = -39    (1)
- 
9
2
B + 
375
37
E = 
273
2
    (2)
 
31
6
C + 
3131
666
E = 
40145
666
    (3)
 D + 
36
37
E = 12    (4)
0 = 0    (5)

Multiply both sides of equation (3) by 18
Divide both sides of equation (3) by 31, get the equation：
         3C + 
101
37
E = 35    (16)
, then subtract both sides of equation (16) from both sides of equation (1), get the equation：
 4A + 2B - 
60
37
E = -74    (1)
- 
9
2
B + 
375
37
E = 
273
2
    (2)
 
31
6
C + 
3131
666
E = 
40145
666
    (3)
 D + 
36
37
E = 12    (4)
0 = 0    (5)

Multiply both sides of equation (2) by 4
Divide both sides of equation (2) by 9, get the equation：
        -2B + 
500
111
E = 
182
3
    (17)
, then add the two sides of equation (17) to both sides of equation (1), get the equation：
 4A + 
320
111
E = - 
40
3
    (1)
- 
9
2
B + 
375
37
E = 
273
2
    (2)
 C + 
101
111
E = 
1295
111
    (3)
 D + 
36
37
E = 12    (4)
0 = 0    (5)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A + 
80
111
E = - 
10
3
    (1)
 B - 
250
111
E = - 
91
3
    (2)
 C + 
101
111
E = 
1295
111
    (3)
 D + 
36
37
E = 12    (4)
0 = 0    (5)


Therefore, the solution of the equation set is:
A = - 
10
3
 - 
80
111
E
B = - 
91
3
 + 
250
111
E
C = 
1295
111
 - 
101
111
E
D = 12 - 
36
37
E


Convert the solution of the equation set to decimals:
A = -3.333333 - 
80
111
E
B = -30.333333 + 
250
111
E
C = 11.666667 - 
101
111
E
D = 12 - 
36
37
E

Where:  E are arbitrary constants.
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