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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 -1B -3C -1D + E = 10    (1)
-3A + 7B -1C -3D -6E = 4    (2)
-3A -1B + 10C = 0    (3)
-1A -1B + 2D = 0    (4)
-1A + B + E = 0    (5)
Question solving process:

Multiply both sides of equation (1) by 3
Divide the two sides of equation (1) by 5, the equation can be obtained:
         3A - 
3
5
B - 
9
5
C - 
3
5
D + 
3
5
E = 6    (6)
, then add the two sides of equation (6) to both sides of equation (2), the equations are reduced to:
 5A -1B -3C -1D + E = 10    (1)
 
32
5
B - 
14
5
C - 
18
5
D - 
27
5
E = 10    (2)
-3A -1B + 10C = 0    (3)
-1A -1B + 2D = 0    (4)
-1A + B + E = 0    (5)

Multiply both sides of equation (1) by 3
Divide the two sides of equation (1) by 5, the equation can be obtained:
         3A - 
3
5
B - 
9
5
C - 
3
5
D + 
3
5
E = 6    (7)
, then add the two sides of equation (7) to both sides of equation (3), the equations are reduced to:
 5A -1B -3C -1D + E = 10    (1)
 
32
5
B - 
14
5
C - 
18
5
D - 
27
5
E = 10    (2)
- 
8
5
B + 
41
5
C - 
3
5
D + 
3
5
E = 6    (3)
-1A -1B + 2D = 0    (4)
-1A + B + E = 0    (5)

Divide the two sides of equation (1) by 5, the equation can be obtained:
         A - 
1
5
B - 
3
5
C - 
1
5
D + 
1
5
E = 2    (8)
, then add the two sides of equation (8) to both sides of equation (4), the equations are reduced to:
 5A -1B -3C -1D + E = 10    (1)
 
32
5
B - 
14
5
C - 
18
5
D - 
27
5
E = 10    (2)
- 
8
5
B + 
41
5
C - 
3
5
D + 
3
5
E = 6    (3)
- 
6
5
B - 
3
5
C + 
9
5
D + 
1
5
E = 2    (4)
-1A + B + E = 0    (5)

Divide the two sides of equation (1) by 5, the equation can be obtained:
         A - 
1
5
B - 
3
5
C - 
1
5
D + 
1
5
E = 2    (9)
, then add the two sides of equation (9) to both sides of equation (5), the equations are reduced to:
 5A -1B -3C -1D + E = 10    (1)
 
32
5
B - 
14
5
C - 
18
5
D - 
27
5
E = 10    (2)
- 
8
5
B + 
41
5
C - 
3
5
D + 
3
5
E = 6    (3)
- 
6
5
B - 
3
5
C + 
9
5
D + 
1
5
E = 2    (4)
 
4
5
B - 
3
5
C - 
1
5
D + 
6
5
E = 2    (5)

Divide the two sides of equation (2) by 4, the equation can be obtained:
         
8
5
B - 
7
10
C - 
9
10
D - 
27
20
E = 
5
2
    (10)
, then add the two sides of equation (10) to both sides of equation (3), the equations are reduced to:
 5A -1B -3C -1D + E = 10    (1)
 
32
5
B - 
14
5
C - 
18
5
D - 
27
5
E = 10    (2)
 
15
2
C - 
3
2
D - 
3
4
E = 
17
2
    (3)
- 
6
5
B - 
3
5
C + 
9
5
D + 
1
5
E = 2    (4)
 
4
5
B - 
3
5
C - 
1
5
D + 
6
5
E = 2    (5)

Multiply both sides of equation (2) by 3
Divide the two sides of equation (2) by 16, the equation can be obtained:
         
6
5
B - 
21
40
C - 
27
40
D - 
81
80
E = 
15
8
    (11)
, then add the two sides of equation (11) to both sides of equation (4), the equations are reduced to:
 5A -1B -3C -1D + E = 10    (1)
 
32
5
B - 
14
5
C - 
18
5
D - 
27
5
E = 10    (2)
 
15
2
C - 
3
2
D - 
3
4
E = 
17
2
    (3)
- 
9
8
C + 
9
8
D - 
13
16
E = 
31
8
    (4)
 
4
5
B - 
3
5
C - 
1
5
D + 
6
5
E = 2    (5)

Divide the two sides of equation (2) by 8, the equation can be obtained:
         
4
5
B - 
7
20
C - 
9
20
D - 
27
40
E = 
5
4
    (12)
, then subtract both sides of equation (12) from both sides of equation (5), the equations are reduced to:
 5A -1B -3C -1D + E = 10    (1)
 
32
5
B - 
14
5
C - 
18
5
D - 
27
5
E = 10    (2)
 
15
2
C - 
3
2
D - 
3
4
E = 
17
2
    (3)
- 
9
8
C + 
9
8
D - 
13
16
E = 
31
8
    (4)
- 
1
4
C + 
1
4
D + 
15
8
E = 
3
4
    (5)

Multiply both sides of equation (3) by 3
Divide the two sides of equation (3) by 20, the equation can be obtained:
         
9
8
C - 
9
40
D - 
9
80
E = 
51
40
    (13)
, then add the two sides of equation (13) to both sides of equation (4), the equations are reduced to:
 5A -1B -3C -1D + E = 10    (1)
 
32
5
B - 
14
5
C - 
18
5
D - 
27
5
E = 10    (2)
 
15
2
C - 
3
2
D - 
3
4
E = 
17
2
    (3)
 
9
10
D - 
37
40
E = 
103
20
    (4)
- 
1
4
C + 
1
4
D + 
15
8
E = 
3
4
    (5)

Divide the two sides of equation (3) by 30, the equation can be obtained:
         
1
4
C - 
1
20
D - 
1
40
E = 
17
60
    (14)
, then add the two sides of equation (14) to both sides of equation (5), the equations are reduced to:
 5A -1B -3C -1D + E = 10    (1)
 
32
5
B - 
14
5
C - 
18
5
D - 
27
5
E = 10    (2)
 
15
2
C - 
3
2
D - 
3
4
E = 
17
2
    (3)
 
9
10
D - 
37
40
E = 
103
20
    (4)
 
1
5
D + 
37
20
E = 
31
30
    (5)

Multiply both sides of equation (4) by 2
Divide the two sides of equation (4) by 9, the equation can be obtained:
         
1
5
D - 
37
180
E = 
103
90
    (15)
, then subtract both sides of equation (15) from both sides of equation (5), the equations are reduced to:
 5A -1B -3C -1D + E = 10    (1)
 
32
5
B - 
14
5
C - 
18
5
D - 
27
5
E = 10    (2)
 
15
2
C - 
3
2
D - 
3
4
E = 
17
2
    (3)
 
9
10
D - 
37
40
E = 
103
20
    (4)
 
37
18
E = - 
1
9
    (5)

Multiply both sides of equation (5) by 9
Divide both sides of equation (5) by 20, get the equation：
         
37
40
E = - 
1
20
    (16)
, then add the two sides of equation (16) to both sides of equation (4), get the equation：
 5A -1B -3C -1D + E = 10    (1)
 
32
5
B - 
14
5
C - 
18
5
D - 
27
5
E = 10    (2)
 
15
2
C - 
3
2
D - 
3
4
E = 
17
2
    (3)
 
9
10
D = 
51
10
    (4)
 
37
18
E = - 
1
9
    (5)

Multiply both sides of equation (5) by 27
Divide both sides of equation (5) by 74, get the equation：
         
3
4
E = - 
3
74
    (17)
, then add the two sides of equation (17) to both sides of equation (3), get the equation：
 5A -1B -3C -1D + E = 10    (1)
 
32
5
B - 
14
5
C - 
18
5
D - 
27
5
E = 10    (2)
 
15
2
C - 
3
2
D = 
313
37
    (3)
 
9
10
D = 
51
10
    (4)
 
37
18
E = - 
1
9
    (5)

Multiply both sides of equation (5) by 486
Divide both sides of equation (5) by 185, get the equation：
         
27
5
E = - 
54
185
    (18)
, then add the two sides of equation (18) to both sides of equation (2), get the equation：
 5A -1B -3C -1D + E = 10    (1)
 
32
5
B - 
14
5
C - 
18
5
D = 
1796
185
    (2)
 
15
2
C - 
3
2
D = 
313
37
    (3)
 
9
10
D = 
51
10
    (4)
 
37
18
E = - 
1
9
    (5)

Multiply both sides of equation (5) by 18
Divide both sides of equation (5) by 37, get the equation：
         E = - 
2
37
    (19)
, then subtract both sides of equation (19) from both sides of equation (1), get the equation：
 5A -1B -3C -1D = 
372
37
    (1)
 
32
5
B - 
14
5
C - 
18
5
D = 
1796
185
    (2)
 
15
2
C - 
3
2
D = 
313
37
    (3)
 
9
10
D = 
51
10
    (4)
 
37
18
E = - 
1
9
    (5)

Multiply both sides of equation (4) by 5
Divide both sides of equation (4) by 3, get the equation：
         
3
2
D = 
17
2
    (20)
, then add the two sides of equation (20) to both sides of equation (3), get the equation：
 5A -1B -3C -1D = 
372
37
    (1)
 
32
5
B - 
14
5
C - 
18
5
D = 
1796
185
    (2)
 
15
2
C = 
1255
74
    (3)
 
9
10
D = 
51
10
    (4)
 E = - 
2
37
    (5)

Multiply both sides of equation (4) by 4, get the equation：
         
18
5
D = 
102
5
    (21)
, then add the two sides of equation (21) to both sides of equation (2), get the equation：
 5A -1B -3C -1D = 
372
37
    (1)
 
32
5
B - 
14
5
C = 
1114
37
    (2)
 
15
2
C = 
1255
74
    (3)
 
9
10
D = 
51
10
    (4)
 E = - 
2
37
    (5)

Multiply both sides of equation (4) by 10
Divide both sides of equation (4) by 9, get the equation：
         D = 
17
3
    (22)
, then add the two sides of equation (22) to both sides of equation (1), get the equation：
 5A -1B -3C = 
1745
111
    (1)
 
32
5
B - 
14
5
C = 
1114
37
    (2)
 
15
2
C = 
1255
74
    (3)
 
9
10
D = 
51
10
    (4)
 E = - 
2
37
    (5)

Multiply both sides of equation (3) by 28
Divide both sides of equation (3) by 75, get the equation：
         
14
5
C = 
3514
555
    (23)
, then add the two sides of equation (23) to both sides of equation (2), get the equation：
 5A -1B -3C = 
1745
111
    (1)
 
32
5
B = 
20224
555
    (2)
 
15
2
C = 
1255
74
    (3)
 D = 
17
3
    (4)
 E = - 
2
37
    (5)

Multiply both sides of equation (3) by 2
Divide both sides of equation (3) by 5, get the equation：
         3C = 
251
37
    (24)
, then add the two sides of equation (24) to both sides of equation (1), get the equation：
 5A -1B = 
2498
111
    (1)
 
32
5
B = 
20224
555
    (2)
 
15
2
C = 
1255
74
    (3)
 D = 
17
3
    (4)
 E = - 
2
37
    (5)

Multiply both sides of equation (2) by 5
Divide both sides of equation (2) by 32, get the equation：
         B = 
632
111
    (25)
, then add the two sides of equation (25) to both sides of equation (1), get the equation：
 5A = 
3130
111
    (1)
 
32
5
B = 
20224
555
    (2)
 C = 
251
111
    (3)
 D = 
17
3
    (4)
 E = - 
2
37
    (5)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
626
111
    (1)
 B = 
632
111
    (2)
 C = 
251
111
    (3)
 D = 
17
3
    (4)
 E = - 
2
37
    (5)


Therefore, the solution of the equation set is:
A = 
626
111
B = 
632
111
C = 
251
111
D = 
17
3
E = - 
2
37


Convert the solution of the equation set to decimals:
A = 5.639640
B = 5.693694
C = 2.261261
D = 5.666667
E = -0.054054

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