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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:
 35A + 45B + 20C + 35D + 30E = 
361
10
    (1)
 45A + 55B + 24C + 40D + 35E = 
1104
25
    (2)
 35A + 35B + 16C + 40D + 24E = 
63
2
    (3)
 45A + 55B + 30C + 40D + 30E = 44    (4)
 50A + 55B + 22C + 35D + 30E = 45    (5)
Question solving process:

Multiply both sides of equation (1) by 9
Divide the two sides of equation (1) by 7, the equation can be obtained:
         45A + 
405
7
B + 
180
7
C + 45D + 
270
7
E = 
3249
70
    (6)
, then subtract both sides of equation (6) from both sides of equation (2), the equations are reduced to:
 35A + 45B + 20C + 35D + 30E = 
361
10
    (1)
- 
20
7
B - 
12
7
C -5D - 
25
7
E = - 
789
350
    (2)
 35A + 35B + 16C + 40D + 24E = 
63
2
    (3)
 45A + 55B + 30C + 40D + 30E = 44    (4)
 50A + 55B + 22C + 35D + 30E = 45    (5)

Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:
 35A + 45B + 20C + 35D + 30E = 
361
10
    (1)
- 
20
7
B - 
12
7
C -5D - 
25
7
E = - 
789
350
    (2)
-10B -4C + 5D -6E = - 
23
5
    (3)
 45A + 55B + 30C + 40D + 30E = 44    (4)
 50A + 55B + 22C + 35D + 30E = 45    (5)

Multiply both sides of equation (1) by 9
Divide the two sides of equation (1) by 7, the equation can be obtained:
         45A + 
405
7
B + 
180
7
C + 45D + 
270
7
E = 
3249
70
    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 35A + 45B + 20C + 35D + 30E = 
361
10
    (1)
- 
20
7
B - 
12
7
C -5D - 
25
7
E = - 
789
350
    (2)
-10B -4C + 5D -6E = - 
23
5
    (3)
- 
20
7
B + 
30
7
C -5D - 
60
7
E = - 
169
70
    (4)
 50A + 55B + 22C + 35D + 30E = 45    (5)

Multiply both sides of equation (1) by 10
Divide the two sides of equation (1) by 7, the equation can be obtained:
         50A + 
450
7
B + 
200
7
C + 50D + 
300
7
E = 
361
7
    (8)
, then subtract both sides of equation (8) from both sides of equation (5), the equations are reduced to:
 35A + 45B + 20C + 35D + 30E = 
361
10
    (1)
- 
20
7
B - 
12
7
C -5D - 
25
7
E = - 
789
350
    (2)
-10B -4C + 5D -6E = - 
23
5
    (3)
- 
20
7
B + 
30
7
C -5D - 
60
7
E = - 
169
70
    (4)
- 
65
7
B - 
46
7
C -15D - 
90
7
E = - 
46
7
    (5)

Multiply both sides of equation (2) by 7
Divide the two sides of equation (2) by 2, the equation can be obtained:
        -10B -6C - 
35
2
D - 
25
2
E = - 
789
100
    (9)
, then subtract both sides of equation (9) from both sides of equation (3), the equations are reduced to:
 35A + 45B + 20C + 35D + 30E = 
361
10
    (1)
- 
20
7
B - 
12
7
C -5D - 
25
7
E = - 
789
350
    (2)
 2C + 
45
2
D + 
13
2
E = 
329
100
    (3)
- 
20
7
B + 
30
7
C -5D - 
60
7
E = - 
169
70
    (4)
- 
65
7
B - 
46
7
C -15D - 
90
7
E = - 
46
7
    (5)

Subtract both sides of equation (2) from both sides of equation (4) ,the equations are reduced to:
 35A + 45B + 20C + 35D + 30E = 
361
10
    (1)
- 
20
7
B - 
12
7
C -5D - 
25
7
E = - 
789
350
    (2)
 2C + 
45
2
D + 
13
2
E = 
329
100
    (3)
 6C -5E = - 
4
25
    (4)
- 
65
7
B - 
46
7
C -15D - 
90
7
E = - 
46
7
    (5)

Multiply both sides of equation (2) by 13
Divide the two sides of equation (2) by 4, the equation can be obtained:
        - 
65
7
B - 
39
7
C - 
65
4
D - 
325
28
E = - 
10257
1400
    (10)
, then subtract both sides of equation (10) from both sides of equation (5), the equations are reduced to:
 35A + 45B + 20C + 35D + 30E = 
361
10
    (1)
- 
20
7
B - 
12
7
C -5D - 
25
7
E = - 
789
350
    (2)
 2C + 
45
2
D + 
13
2
E = 
329
100
    (3)
 6C -5E = - 
4
25
    (4)
-1C + 
5
4
D - 
5
4
E = 
151
200
    (5)

Multiply both sides of equation (3) by 3, the equation can be obtained:
         6C + 
135
2
D + 
39
2
E = 
987
100
    (11)
, then subtract both sides of equation (11) from both sides of equation (4), the equations are reduced to:
 35A + 45B + 20C + 35D + 30E = 
361
10
    (1)
- 
20
7
B - 
12
7
C -5D - 
25
7
E = - 
789
350
    (2)
 2C + 
45
2
D + 
13
2
E = 
329
100
    (3)
- 
135
2
D - 
49
2
E = - 
1003
100
    (4)
-1C + 
5
4
D - 
5
4
E = 
151
200
    (5)

Divide the two sides of equation (3) by 2, the equation can be obtained:
         C + 
45
4
D + 
13
4
E = 
329
200
    (12)
, then add the two sides of equation (12) to both sides of equation (5), the equations are reduced to:
 35A + 45B + 20C + 35D + 30E = 
361
10
    (1)
- 
20
7
B - 
12
7
C -5D - 
25
7
E = - 
789
350
    (2)
 2C + 
45
2
D + 
13
2
E = 
329
100
    (3)
- 
135
2
D - 
49
2
E = - 
1003
100
    (4)
 
25
2
D + 2E = 
12
5
    (5)

Multiply both sides of equation (4) by 5
Divide the two sides of equation (4) by 27, the equation can be obtained:
        - 
25
2
D - 
245
54
E = - 
1003
540
    (13)
, then add the two sides of equation (13) to both sides of equation (5), the equations are reduced to:
 35A + 45B + 20C + 35D + 30E = 
361
10
    (1)
- 
20
7
B - 
12
7
C -5D - 
25
7
E = - 
789
350
    (2)
 2C + 
45
2
D + 
13
2
E = 
329
100
    (3)
- 
135
2
D - 
49
2
E = - 
1003
100
    (4)
- 
137
54
E = 
293
540
    (5)

Multiply both sides of equation (5) by 1323
Divide both sides of equation (5) by 137, get the equation：
        - 
6713
274
E = 
14357
2740
    (14)
, then subtract both sides of equation (14) from both sides of equation (4), get the equation：
 35A + 45B + 20C + 35D + 30E = 
361
10
    (1)
- 
20
7
B - 
12
7
C -5D - 
25
7
E = - 
789
350
    (2)
 2C + 
45
2
D + 
13
2
E = 
329
100
    (3)
- 
135
2
D = - 
52299
3425
    (4)
- 
137
54
E = 
293
540
    (5)

Multiply both sides of equation (5) by 351
Divide both sides of equation (5) by 137, get the equation：
        - 
1781
274
E = 
3809
2740
    (15)
, then add the two sides of equation (15) to both sides of equation (3), get the equation：
 35A + 45B + 20C + 35D + 30E = 
361
10
    (1)
- 
20
7
B - 
12
7
C -5D - 
25
7
E = - 
789
350
    (2)
 2C + 
45
2
D = 
32059
6850
    (3)
- 
135
2
D = - 
52299
3425
    (4)
- 
137
54
E = 
293
540
    (5)

Multiply both sides of equation (5) by 1350
Divide both sides of equation (5) by 959, get the equation：
        - 
3425
959
E = 
1465
1918
    (16)
, then subtract both sides of equation (16) from both sides of equation (2), get the equation：
 35A + 45B + 20C + 35D + 30E = 
361
10
    (1)
- 
20
7
B - 
12
7
C -5D = - 
10337
3425
    (2)
 2C + 
45
2
D = 
32059
6850
    (3)
- 
135
2
D = - 
52299
3425
    (4)
- 
137
54
E = 
293
540
    (5)

Multiply both sides of equation (5) by 1620
Divide both sides of equation (5) by 137, get the equation：
        - 
4110
137
E = 
879
137
    (17)
, then add the two sides of equation (17) to both sides of equation (1), get the equation：
 35A + 45B + 20C + 35D = 
58247
1370
    (1)
- 
20
7
B - 
12
7
C -5D = - 
10337
3425
    (2)
 2C + 
45
2
D = 
32059
6850
    (3)
- 
135
2
D = - 
52299
3425
    (4)
- 
137
54
E = 
293
540
    (5)

Divide both sides of equation (4) by 3, get the equation：
        - 
45
2
D = - 
17433
3425
    (18)
, then add the two sides of equation (18) to both sides of equation (3), get the equation：
 35A + 45B + 20C + 35D = 
58247
1370
    (1)
- 
20
7
B - 
12
7
C -5D = - 
10337
3425
    (2)
 2C = - 
2807
6850
    (3)
- 
135
2
D = - 
52299
3425
    (4)
 E = - 
293
1370
    (5)

Multiply both sides of equation (4) by 2
Divide both sides of equation (4) by 27, get the equation：
        -5D = - 
3874
3425
    (19)
, then subtract both sides of equation (19) from both sides of equation (2), get the equation：
 35A + 45B + 20C + 35D = 
58247
1370
    (1)
- 
20
7
B - 
12
7
C = - 
6463
3425
    (2)
 2C = - 
2807
6850
    (3)
- 
135
2
D = - 
52299
3425
    (4)
 E = - 
293
1370
    (5)

Multiply both sides of equation (4) by 14
Divide both sides of equation (4) by 27, get the equation：
        -35D = - 
27118
3425
    (20)
, then add the two sides of equation (20) to both sides of equation (1), get the equation：
 35A + 45B + 20C = 
236999
6850
    (1)
- 
20
7
B - 
12
7
C = - 
6463
3425
    (2)
 2C = - 
2807
6850
    (3)
- 
135
2
D = - 
52299
3425
    (4)
 E = - 
293
1370
    (5)

Multiply both sides of equation (3) by 6
Divide both sides of equation (3) by 7, get the equation：
         
12
7
C = - 
1203
3425
    (21)
, then add the two sides of equation (21) to both sides of equation (2), get the equation：
 35A + 45B + 20C = 
236999
6850
    (1)
- 
20
7
B = - 
7666
3425
    (2)
 2C = - 
2807
6850
    (3)
 D = 
3874
17125
    (4)
 E = - 
293
1370
    (5)

Multiply both sides of equation (3) by 10, get the equation：
         20C = - 
2807
685
    (22)
, then subtract both sides of equation (22) from both sides of equation (1), get the equation：
 35A + 45B = 
265069
6850
    (1)
- 
20
7
B = - 
7666
3425
    (2)
 2C = - 
2807
6850
    (3)
 D = 
3874
17125
    (4)
 E = - 
293
1370
    (5)

Multiply both sides of equation (2) by 63
Divide both sides of equation (2) by 4, get the equation：
        -45B = - 
241479
6850
    (23)
, then add the two sides of equation (23) to both sides of equation (1), get the equation：
 35A = 
2359
685
    (1)
- 
20
7
B = - 
7666
3425
    (2)
 C = - 
2807
13700
    (3)
 D = 
3874
17125
    (4)
 E = - 
293
1370
    (5)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
337
3425
    (1)
 B = 
26831
34250
    (2)
 C = - 
2807
13700
    (3)
 D = 
3874
17125
    (4)
 E = - 
293
1370
    (5)


Therefore, the solution of the equation set is:
A = 
337
3425
B = 
26831
34250
C = - 
2807
13700
D = 
3874
17125
E = - 
293
1370


Convert the solution of the equation set to decimals:
A = 0.098394
B = 0.783387
C = -0.204891
D = 0.226219
E = -0.213869

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