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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:
 20A + 19G + J = 1    (1)
 20B + 19H + K = 25    (2)
 20C + 19I + L = 20    (3)
 3D + 8G + J = 3    (4)
 24D + 4G + J = 14    (5)
 3E + 8H + K = 18    (6)
 24E + 4H + K = 15    (7)
 3F + 8I + L = 17    (8)
 24F + 4I + L = 11    (9)
 18A + 15D + 11G + J = 12    (10)
 18B + 15E + 11H + K = 18    (11)
 18C + 15F + 11I + L = 8    (12)
Question solving process:

Multiply both sides of equation (1) by 9
Divide the two sides of equation (1) by 10, the equation can be obtained:
         18A + 
171
10
G + 
9
10
J = 
9
10
    (13)
, then subtract both sides of equation (13) from both sides of equation (10), the equations are reduced to:
 20A + 19G + J = 1    (1)
 20B + 19H + K = 25    (2)
 20C + 19I + L = 20    (3)
 3D + 8G + J = 3    (4)
 24D + 4G + J = 14    (5)
 3E + 8H + K = 18    (6)
 24E + 4H + K = 15    (7)
 3F + 8I + L = 17    (8)
 24F + 4I + L = 11    (9)
 15D - 
61
10
G + 
1
10
J = 
111
10
    (10)
 18B + 15E + 11H + K = 18    (11)
 18C + 15F + 11I + L = 8    (12)

Multiply both sides of equation (2) by 9
Divide the two sides of equation (2) by 10, the equation can be obtained:
         18B + 
171
10
H + 
9
10
K = 
45
2
    (14)
, then subtract both sides of equation (14) from both sides of equation (11), the equations are reduced to:
 20A + 19G + J = 1    (1)
 20B + 19H + K = 25    (2)
 20C + 19I + L = 20    (3)
 3D + 8G + J = 3    (4)
 24D + 4G + J = 14    (5)
 3E + 8H + K = 18    (6)
 24E + 4H + K = 15    (7)
 3F + 8I + L = 17    (8)
 24F + 4I + L = 11    (9)
 15D - 
61
10
G + 
1
10
J = 
111
10
    (10)
 15E - 
61
10
H + 
1
10
K = - 
9
2
    (11)
 18C + 15F + 11I + L = 8    (12)

Multiply both sides of equation (3) by 9
Divide the two sides of equation (3) by 10, the equation can be obtained:
         18C + 
171
10
I + 
9
10
L = 18    (15)
, then subtract both sides of equation (15) from both sides of equation (12), the equations are reduced to:
 20A + 19G + J = 1    (1)
 20B + 19H + K = 25    (2)
 20C + 19I + L = 20    (3)
 3D + 8G + J = 3    (4)
 24D + 4G + J = 14    (5)
 3E + 8H + K = 18    (6)
 24E + 4H + K = 15    (7)
 3F + 8I + L = 17    (8)
 24F + 4I + L = 11    (9)
 15D - 
61
10
G + 
1
10
J = 
111
10
    (10)
 15E - 
61
10
H + 
1
10
K = - 
9
2
    (11)
 15F - 
61
10
I + 
1
10
L = -10    (12)

Multiply both sides of equation (4) by 8, the equation can be obtained:
         24D + 64G + 8J = 24    (16)
, then subtract both sides of equation (16) from both sides of equation (5), the equations are reduced to:
 20A + 19G + J = 1    (1)
 20B + 19H + K = 25    (2)
 20C + 19I + L = 20    (3)
 3D + 8G + J = 3    (4)
-60G -7J = -10    (5)
 3E + 8H + K = 18    (6)
 24E + 4H + K = 15    (7)
 3F + 8I + L = 17    (8)
 24F + 4I + L = 11    (9)
 15D - 
61
10
G + 
1
10
J = 
111
10
    (10)
 15E - 
61
10
H + 
1
10
K = - 
9
2
    (11)
 15F - 
61
10
I + 
1
10
L = -10    (12)

Multiply both sides of equation (4) by 5, the equation can be obtained:
         15D + 40G + 5J = 15    (17)
, then subtract both sides of equation (17) from both sides of equation (10), the equations are reduced to:
 20A + 19G + J = 1    (1)
 20B + 19H + K = 25    (2)
 20C + 19I + L = 20    (3)
 3D + 8G + J = 3    (4)
-60G -7J = -10    (5)
 3E + 8H + K = 18    (6)
 24E + 4H + K = 15    (7)
 3F + 8I + L = 17    (8)
 24F + 4I + L = 11    (9)
- 
461
10
G - 
49
10
J = - 
39
10
    (10)
 15E - 
61
10
H + 
1
10
K = - 
9
2
    (11)
 15F - 
61
10
I + 
1
10
L = -10    (12)

交After the exchange of equation (5) and equation (6)， the equation system becomes:
 20A + 19G + J = 1    (1)
 20B + 19H + K = 25    (2)
 20C + 19I + L = 20    (3)
 3D + 8G + J = 3    (4)
 3E + 8H + K = 18    (5)
-60G -7J = -10    (6)
 24E + 4H + K = 15    (7)
 3F + 8I + L = 17    (8)
 24F + 4I + L = 11    (9)
- 
461
10
G - 
49
10
J = - 
39
10
    (10)
 15E - 
61
10
H + 
1
10
K = - 
9
2
    (11)
 15F - 
61
10
I + 
1
10
L = -10    (12)

Multiply both sides of equation (5) by 8, the equation can be obtained:
         24E + 64H + 8K = 144    (18)
, then subtract both sides of equation (18) from both sides of equation (7), the equations are reduced to:
 20A + 19G + J = 1    (1)
 20B + 19H + K = 25    (2)
 20C + 19I + L = 20    (3)
 3D + 8G + J = 3    (4)
 3E + 8H + K = 18    (5)
-60G -7J = -10    (6)
-60H -7K = -129    (7)
 3F + 8I + L = 17    (8)
 24F + 4I + L = 11    (9)
- 
461
10
G - 
49
10
J = - 
39
10
    (10)
 15E - 
61
10
H + 
1
10
K = - 
9
2
    (11)
 15F - 
61
10
I + 
1
10
L = -10    (12)

Multiply both sides of equation (5) by 5, the equation can be obtained:
         15E + 40H + 5K = 90    (19)
, then subtract both sides of equation (19) from both sides of equation (11), the equations are reduced to:
 20A + 19G + J = 1    (1)
 20B + 19H + K = 25    (2)
 20C + 19I + L = 20    (3)
 3D + 8G + J = 3    (4)
 3E + 8H + K = 18    (5)
-60G -7J = -10    (6)
-60H -7K = -129    (7)
 3F + 8I + L = 17    (8)
 24F + 4I + L = 11    (9)
- 
461
10
G - 
49
10
J = - 
39
10
    (10)
- 
461
10
H - 
49
10
K = - 
189
2
    (11)
 15F - 
61
10
I + 
1
10
L = -10    (12)

交After the exchange of equation (6) and equation (8)， the equation system becomes:
 20A + 19G + J = 1    (1)
 20B + 19H + K = 25    (2)
 20C + 19I + L = 20    (3)
 3D + 8G + J = 3    (4)
 3E + 8H + K = 18    (5)
 3F + 8I + L = 17    (6)
-60H -7K = -129    (7)
-60G -7J = -10    (8)
 24F + 4I + L = 11    (9)
- 
461
10
G - 
49
10
J = - 
39
10
    (10)
- 
461
10
H - 
49
10
K = - 
189
2
    (11)
 15F - 
61
10
I + 
1
10
L = -10    (12)

Multiply both sides of equation (6) by 8, the equation can be obtained:
         24F + 64I + 8L = 136    (20)
, then subtract both sides of equation (20) from both sides of equation (9), the equations are reduced to:
 20A + 19G + J = 1    (1)
 20B + 19H + K = 25    (2)
 20C + 19I + L = 20    (3)
 3D + 8G + J = 3    (4)
 3E + 8H + K = 18    (5)
 3F + 8I + L = 17    (6)
-60H -7K = -129    (7)
-60G -7J = -10    (8)
-60I -7L = -125    (9)
- 
461
10
G - 
49
10
J = - 
39
10
    (10)
- 
461
10
H - 
49
10
K = - 
189
2
    (11)
 15F - 
61
10
I + 
1
10
L = -10    (12)

Multiply both sides of equation (6) by 5, the equation can be obtained:
         15F + 40I + 5L = 85    (21)
, then subtract both sides of equation (21) from both sides of equation (12), the equations are reduced to:
 20A + 19G + J = 1    (1)
 20B + 19H + K = 25    (2)
 20C + 19I + L = 20    (3)
 3D + 8G + J = 3    (4)
 3E + 8H + K = 18    (5)
 3F + 8I + L = 17    (6)
-60H -7K = -129    (7)
-60G -7J = -10    (8)
-60I -7L = -125    (9)
- 
461
10
G - 
49
10
J = - 
39
10
    (10)
- 
461
10
H - 
49
10
K = - 
189
2
    (11)
- 
461
10
I - 
49
10
L = -95    (12)

交After the exchange of equation (7) and equation (8)， the equation system becomes:
 20A + 19G + J = 1    (1)
 20B + 19H + K = 25    (2)
 20C + 19I + L = 20    (3)
 3D + 8G + J = 3    (4)
 3E + 8H + K = 18    (5)
 3F + 8I + L = 17    (6)
-60G -7J = -10    (7)
-60H -7K = -129    (8)
-60I -7L = -125    (9)
- 
461
10
G - 
49
10
J = - 
39
10
    (10)
- 
461
10
H - 
49
10
K = - 
189
2
    (11)
- 
461
10
I - 
49
10
L = -95    (12)

Multiply both sides of equation (7) by 461
Divide the two sides of equation (7) by 600, the equation can be obtained:
        - 
461
10
G - 
3227
600
J = - 
461
60
    (22)
, then subtract both sides of equation (22) from both sides of equation (10), the equations are reduced to:
 20A + 19G + J = 1    (1)
 20B + 19H + K = 25    (2)
 20C + 19I + L = 20    (3)
 3D + 8G + J = 3    (4)
 3E + 8H + K = 18    (5)
 3F + 8I + L = 17    (6)
-60G -7J = -10    (7)
-60H -7K = -129    (8)
-60I -7L = -125    (9)
 
287
600
J = 
227
60
    (10)
- 
461
10
H - 
49
10
K = - 
189
2
    (11)
- 
461
10
I - 
49
10
L = -95    (12)

Multiply both sides of equation (8) by 461
Divide the two sides of equation (8) by 600, the equation can be obtained:
        - 
461
10
H - 
3227
600
K = - 
19823
200
    (23)
, then subtract both sides of equation (23) from both sides of equation (11), the equations are reduced to:
 20A + 19G + J = 1    (1)
 20B + 19H + K = 25    (2)
 20C + 19I + L = 20    (3)
 3D + 8G + J = 3    (4)
 3E + 8H + K = 18    (5)
 3F + 8I + L = 17    (6)
-60G -7J = -10    (7)
-60H -7K = -129    (8)
-60I -7L = -125    (9)
 
287
600
J = 
227
60
    (10)
 
287
600
K = 
923
200
    (11)
- 
461
10
I - 
49
10
L = -95    (12)

Multiply both sides of equation (9) by 461
Divide the two sides of equation (9) by 600, the equation can be obtained:
        - 
461
10
I - 
3227
600
L = - 
2305
24
    (24)
, then subtract both sides of equation (24) from both sides of equation (12), the equations are reduced to:
 20A + 19G + J = 1    (1)
 20B + 19H + K = 25    (2)
 20C + 19I + L = 20    (3)
 3D + 8G + J = 3    (4)
 3E + 8H + K = 18    (5)
 3F + 8I + L = 17    (6)
-60G -7J = -10    (7)
-60H -7K = -129    (8)
-60I -7L = -125    (9)
 
287
600
J = 
227
60
    (10)
 
287
600
K = 
923
200
    (11)
 
287
600
L = 
25
24
    (12)

Multiply both sides of equation (12) by 600
Divide both sides of equation (12) by 41, get the equation：
         7L = 
625
41
    (25)
, then add the two sides of equation (25) to both sides of equation (9), get the equation：
 20A + 19G + J = 1    (1)
 20B + 19H + K = 25    (2)
 20C + 19I + L = 20    (3)
 3D + 8G + J = 3    (4)
 3E + 8H + K = 18    (5)
 3F + 8I + L = 17    (6)
-60G -7J = -10    (7)
-60H -7K = -129    (8)
-60I = - 
4500
41
    (9)
 
287
600
J = 
227
60
    (10)
 
287
600
K = 
923
200
    (11)
 
287
600
L = 
25
24
    (12)

Multiply both sides of equation (12) by 600
Divide both sides of equation (12) by 287, get the equation：
         L = 
625
287
    (26)
, then subtract both sides of equation (26) from both sides of equation (6), get the equation：
 20A + 19G + J = 1    (1)
 20B + 19H + K = 25    (2)
 20C + 19I + L = 20    (3)
 3D + 8G + J = 3    (4)
 3E + 8H + K = 18    (5)
 3F + 8I = 
4254
287
    (6)
-60G -7J = -10    (7)
-60H -7K = -129    (8)
-60I = - 
4500
41
    (9)
 
287
600
J = 
227
60
    (10)
 
287
600
K = 
923
200
    (11)
 
287
600
L = 
25
24
    (12)

Multiply both sides of equation (12) by 600
Divide both sides of equation (12) by 287, get the equation：
         L = 
625
287
    (27)
, then subtract both sides of equation (27) from both sides of equation (3), get the equation：
 20A + 19G + J = 1    (1)
 20B + 19H + K = 25    (2)
 20C + 19I = 
5115
287
    (3)
 3D + 8G + J = 3    (4)
 3E + 8H + K = 18    (5)
 3F + 8I = 
4254
287
    (6)
-60G -7J = -10    (7)
-60H -7K = -129    (8)
-60I = - 
4500
41
    (9)
 
287
600
J = 
227
60
    (10)
 
287
600
K = 
923
200
    (11)
 
287
600
L = 
25
24
    (12)

Multiply both sides of equation (11) by 600
Divide both sides of equation (11) by 41, get the equation：
         7K = 
2769
41
    (28)
, then add the two sides of equation (28) to both sides of equation (8), get the equation：
 20A + 19G + J = 1    (1)
 20B + 19H + K = 25    (2)
 20C + 19I = 
5115
287
    (3)
 3D + 8G + J = 3    (4)
 3E + 8H + K = 18    (5)
 3F + 8I = 
4254
287
    (6)
-60G -7J = -10    (7)
-60H = - 
2520
41
    (8)
-60I = - 
4500
41
    (9)
 
287
600
J = 
227
60
    (10)
 
287
600
K = 
923
200
    (11)
 L = 
625
287
    (12)

Multiply both sides of equation (11) by 600
Divide both sides of equation (11) by 287, get the equation：
         K = 
2769
287
    (29)
, then subtract both sides of equation (29) from both sides of equation (5), get the equation：
 20A + 19G + J = 1    (1)
 20B + 19H + K = 25    (2)
 20C + 19I = 
5115
287
    (3)
 3D + 8G + J = 3    (4)
 3E + 8H = 
2397
287
    (5)
 3F + 8I = 
4254
287
    (6)
-60G -7J = -10    (7)
-60H = - 
2520
41
    (8)
-60I = - 
4500
41
    (9)
 
287
600
J = 
227
60
    (10)
 
287
600
K = 
923
200
    (11)
 L = 
625
287
    (12)

Multiply both sides of equation (11) by 600
Divide both sides of equation (11) by 287, get the equation：
         K = 
2769
287
    (30)
, then subtract both sides of equation (30) from both sides of equation (2), get the equation：
 20A + 19G + J = 1    (1)
 20B + 19H = 
4406
287
    (2)
 20C + 19I = 
5115
287
    (3)
 3D + 8G + J = 3    (4)
 3E + 8H = 
2397
287
    (5)
 3F + 8I = 
4254
287
    (6)
-60G -7J = -10    (7)
-60H = - 
2520
41
    (8)
-60I = - 
4500
41
    (9)
 
287
600
J = 
227
60
    (10)
 
287
600
K = 
923
200
    (11)
 L = 
625
287
    (12)

Multiply both sides of equation (10) by 600
Divide both sides of equation (10) by 41, get the equation：
         7J = 
2270
41
    (31)
, then add the two sides of equation (31) to both sides of equation (7), get the equation：
 20A + 19G + J = 1    (1)
 20B + 19H = 
4406
287
    (2)
 20C + 19I = 
5115
287
    (3)
 3D + 8G + J = 3    (4)
 3E + 8H = 
2397
287
    (5)
 3F + 8I = 
4254
287
    (6)
-60G = 
1860
41
    (7)
-60H = - 
2520
41
    (8)
-60I = - 
4500
41
    (9)
 
287
600
J = 
227
60
    (10)
 K = 
2769
287
    (11)
 L = 
625
287
    (12)

Multiply both sides of equation (10) by 600
Divide both sides of equation (10) by 287, get the equation：
         J = 
2270
287
    (32)
, then subtract both sides of equation (32) from both sides of equation (4), get the equation：
 20A + 19G + J = 1    (1)
 20B + 19H = 
4406
287
    (2)
 20C + 19I = 
5115
287
    (3)
 3D + 8G = - 
1409
287
    (4)
 3E + 8H = 
2397
287
    (5)
 3F + 8I = 
4254
287
    (6)
-60G = 
1860
41
    (7)
-60H = - 
2520
41
    (8)
-60I = - 
4500
41
    (9)
 
287
600
J = 
227
60
    (10)
 K = 
2769
287
    (11)
 L = 
625
287
    (12)

Multiply both sides of equation (10) by 600
Divide both sides of equation (10) by 287, get the equation：
         J = 
2270
287
    (33)
, then subtract both sides of equation (33) from both sides of equation (1), get the equation：
 20A + 19G = - 
1983
287
    (1)
 20B + 19H = 
4406
287
    (2)
 20C + 19I = 
5115
287
    (3)
 3D + 8G = - 
1409
287
    (4)
 3E + 8H = 
2397
287
    (5)
 3F + 8I = 
4254
287
    (6)
-60G = 
1860
41
    (7)
-60H = - 
2520
41
    (8)
-60I = - 
4500
41
    (9)
 
287
600
J = 
227
60
    (10)
 K = 
2769
287
    (11)
 L = 
625
287
    (12)

Multiply both sides of equation (9) by 2
Divide both sides of equation (9) by 15, get the equation：
        -8I = - 
600
41
    (34)
, then add the two sides of equation (34) to both sides of equation (6), get the equation：
 20A + 19G = - 
1983
287
    (1)
 20B + 19H = 
4406
287
    (2)
 20C + 19I = 
5115
287
    (3)
 3D + 8G = - 
1409
287
    (4)
 3E + 8H = 
2397
287
    (5)
 3F = 
54
287
    (6)
-60G = 
1860
41
    (7)
-60H = - 
2520
41
    (8)
-60I = - 
4500
41
    (9)
 J = 
2270
287
    (10)
 K = 
2769
287
    (11)
 L = 
625
287
    (12)

Multiply both sides of equation (9) by 19
Divide both sides of equation (9) by 60, get the equation：
        -19I = - 
1425
41
    (35)
, then add the two sides of equation (35) to both sides of equation (3), get the equation：
 20A + 19G = - 
1983
287
    (1)
 20B + 19H = 
4406
287
    (2)
 20C = - 
4860
287
    (3)
 3D + 8G = - 
1409
287
    (4)
 3E + 8H = 
2397
287
    (5)
 3F = 
54
287
    (6)
-60G = 
1860
41
    (7)
-60H = - 
2520
41
    (8)
-60I = - 
4500
41
    (9)
 J = 
2270
287
    (10)
 K = 
2769
287
    (11)
 L = 
625
287
    (12)

Multiply both sides of equation (8) by 2
Divide both sides of equation (8) by 15, get the equation：
        -8H = - 
336
41
    (36)
, then add the two sides of equation (36) to both sides of equation (5), get the equation：
 20A + 19G = - 
1983
287
    (1)
 20B + 19H = 
4406
287
    (2)
 20C = - 
4860
287
    (3)
 3D + 8G = - 
1409
287
    (4)
 3E = 
45
287
    (5)
 3F = 
54
287
    (6)
-60G = 
1860
41
    (7)
-60H = - 
2520
41
    (8)
 I = 
75
41
    (9)
 J = 
2270
287
    (10)
 K = 
2769
287
    (11)
 L = 
625
287
    (12)

Multiply both sides of equation (8) by 19
Divide both sides of equation (8) by 60, get the equation：
        -19H = - 
798
41
    (37)
, then add the two sides of equation (37) to both sides of equation (2), get the equation：
 20A + 19G = - 
1983
287
    (1)
 20B = - 
1180
287
    (2)
 20C = - 
4860
287
    (3)
 3D + 8G = - 
1409
287
    (4)
 3E = 
45
287
    (5)
 3F = 
54
287
    (6)
-60G = 
1860
41
    (7)
-60H = - 
2520
41
    (8)
 I = 
75
41
    (9)
 J = 
2270
287
    (10)
 K = 
2769
287
    (11)
 L = 
625
287
    (12)

Multiply both sides of equation (7) by 2
Divide both sides of equation (7) by 15, get the equation：
        -8G = 
248
41
    (38)
, then add the two sides of equation (38) to both sides of equation (4), get the equation：
 20A + 19G = - 
1983
287
    (1)
 20B = - 
1180
287
    (2)
 20C = - 
4860
287
    (3)
 3D = 
327
287
    (4)
 3E = 
45
287
    (5)
 3F = 
54
287
    (6)
-60G = 
1860
41
    (7)
 H = 
42
41
    (8)
 I = 
75
41
    (9)
 J = 
2270
287
    (10)
 K = 
2769
287
    (11)
 L = 
625
287
    (12)

Multiply both sides of equation (7) by 19
Divide both sides of equation (7) by 60, get the equation：
        -19G = 
589
41
    (39)
, then add the two sides of equation (39) to both sides of equation (1), get the equation：
 20A = 
2140
287
    (1)
 20B = - 
1180
287
    (2)
 20C = - 
4860
287
    (3)
 3D = 
327
287
    (4)
 3E = 
45
287
    (5)
 3F = 
54
287
    (6)
-60G = 
1860
41
    (7)
 H = 
42
41
    (8)
 I = 
75
41
    (9)
 J = 
2270
287
    (10)
 K = 
2769
287
    (11)
 L = 
625
287
    (12)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
107
287
    (1)
 B = - 
59
287
    (2)
 C = - 
243
287
    (3)
 D = 
109
287
    (4)
 E = 
15
287
    (5)
 F = 
18
287
    (6)
 G = - 
31
41
    (7)
 H = 
42
41
    (8)
 I = 
75
41
    (9)
 J = 
2270
287
    (10)
 K = 
2769
287
    (11)
 L = 
625
287
    (12)


Therefore, the solution of the equation set is:
A = 
107
287
B = - 
59
287
C = - 
243
287
D = 
109
287
E = 
15
287
F = 
18
287
G = - 
31
41
H = 
42
41
I = 
75
41
J = 
2270
287
K = 
2769
287
L = 
625
287


Convert the solution of the equation set to decimals:
A = 0.372822
B = -0.205575
C = -0.846690
D = 0.379791
E = 0.052265
F = 0.062718
G = -0.756098
H = 1.024390
I = 1.829268
J = 7.909408
K = 9.648084
L = 2.177700

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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  New addition:Lenders ToolBox module（Specific location：Math OP > Lenders ToolBox ），welcome。