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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:
 350A -250B -3G = 0    (1)
-250A + 250B + G = -1    (2)
 75C -75D -1G = 0    (3)
-75C + 135D + 500E = 0    (4)
 B -1F = 0    (5)
-1D + E -1F = 0    (6)
 300B -300C -1G = 0    (7)
Question solving process:

Multiply both sides of equation (1) by 5
Divide the two sides of equation (1) by 7, the equation can be obtained:
         250A - 
1250
7
B - 
15
7
G = 0    (8)
, then add the two sides of equation (8) to both sides of equation (2), the equations are reduced to:
 350A -250B -3G = 0    (1)
 
500
7
B - 
8
7
G = -1    (2)
 75C -75D -1G = 0    (3)
-75C + 135D + 500E = 0    (4)
 B -1F = 0    (5)
-1D + E -1F = 0    (6)
 300B -300C -1G = 0    (7)

Multiply both sides of equation (2) by 7
Divide the two sides of equation (2) by 500, the equation can be obtained:
         B - 
2
125
G = - 
7
500
    (9)
, then subtract both sides of equation (9) from both sides of equation (5), the equations are reduced to:
 350A -250B -3G = 0    (1)
 
500
7
B - 
8
7
G = -1    (2)
 75C -75D -1G = 0    (3)
-75C + 135D + 500E = 0    (4)
-1F + 
2
125
G = 
7
500
    (5)
-1D + E -1F = 0    (6)
 300B -300C -1G = 0    (7)

Multiply both sides of equation (2) by 21
Divide the two sides of equation (2) by 5, the equation can be obtained:
         300B - 
24
5
G = - 
21
5
    (10)
, then subtract both sides of equation (10) from both sides of equation (7), the equations are reduced to:
 350A -250B -3G = 0    (1)
 
500
7
B - 
8
7
G = -1    (2)
 75C -75D -1G = 0    (3)
-75C + 135D + 500E = 0    (4)
-1F + 
2
125
G = 
7
500
    (5)
-1D + E -1F = 0    (6)
-300C + 
19
5
G = 
21
5
    (7)

Add both sides of equation (3) to both sides of equation (4) ,the equations are reduced to:
 350A -250B -3G = 0    (1)
 
500
7
B - 
8
7
G = -1    (2)
 75C -75D -1G = 0    (3)
 60D + 500E -1G = 0    (4)
-1F + 
2
125
G = 
7
500
    (5)
-1D + E -1F = 0    (6)
-300C + 
19
5
G = 
21
5
    (7)

Multiply both sides of equation (3) by 4, the equation can be obtained:
         300C -300D -4G = 0    (11)
, then add the two sides of equation (11) to both sides of equation (7), the equations are reduced to:
 350A -250B -3G = 0    (1)
 
500
7
B - 
8
7
G = -1    (2)
 75C -75D -1G = 0    (3)
 60D + 500E -1G = 0    (4)
-1F + 
2
125
G = 
7
500
    (5)
-1D + E -1F = 0    (6)
-300D - 
1
5
G = 
21
5
    (7)

Divide the two sides of equation (4) by 60, the equation can be obtained:
         D + 
25
3
E - 
1
60
G = 0    (12)
, then add the two sides of equation (12) to both sides of equation (6), the equations are reduced to:
 350A -250B -3G = 0    (1)
 
500
7
B - 
8
7
G = -1    (2)
 75C -75D -1G = 0    (3)
 60D + 500E -1G = 0    (4)
-1F + 
2
125
G = 
7
500
    (5)
 
28
3
E -1F - 
1
60
G = 0    (6)
-300D - 
1
5
G = 
21
5
    (7)

Multiply both sides of equation (4) by 5, the equation can be obtained:
         300D + 2500E -5G = 0    (13)
, then add the two sides of equation (13) to both sides of equation (7), the equations are reduced to:
 350A -250B -3G = 0    (1)
 
500
7
B - 
8
7
G = -1    (2)
 75C -75D -1G = 0    (3)
 60D + 500E -1G = 0    (4)
-1F + 
2
125
G = 
7
500
    (5)
 
28
3
E -1F - 
1
60
G = 0    (6)
 2500E - 
26
5
G = 
21
5
    (7)

交After the exchange of equation (5) and equation (6)， the equation system becomes:
 350A -250B -3G = 0    (1)
 
500
7
B - 
8
7
G = -1    (2)
 75C -75D -1G = 0    (3)
 60D + 500E -1G = 0    (4)
 
28
3
E -1F - 
1
60
G = 0    (5)
-1F + 
2
125
G = 
7
500
    (6)
 2500E - 
26
5
G = 
21
5
    (7)

Multiply both sides of equation (5) by 1875
Divide the two sides of equation (5) by 7, the equation can be obtained:
         2500E - 
1875
7
F - 
125
28
G = 0    (14)
, then subtract both sides of equation (14) from both sides of equation (7), the equations are reduced to:
 350A -250B -3G = 0    (1)
 
500
7
B - 
8
7
G = -1    (2)
 75C -75D -1G = 0    (3)
 60D + 500E -1G = 0    (4)
 
28
3
E -1F - 
1
60
G = 0    (5)
-1F + 
2
125
G = 
7
500
    (6)
 
1875
7
F - 
103
140
G = 
21
5
    (7)

Multiply both sides of equation (6) by 1875
Divide the two sides of equation (6) by 7, the equation can be obtained:
        - 
1875
7
F + 
30
7
G = 
15
4
    (15)
, then add the two sides of equation (15) to both sides of equation (7), the equations are reduced to:
 350A -250B -3G = 0    (1)
 
500
7
B - 
8
7
G = -1    (2)
 75C -75D -1G = 0    (3)
 60D + 500E -1G = 0    (4)
 
28
3
E -1F - 
1
60
G = 0    (5)
-1F + 
2
125
G = 
7
500
    (6)
 
71
20
G = 
159
20
    (7)

Multiply both sides of equation (7) by 8
Divide both sides of equation (7) by 1775, get the equation：
         
2
125
G = 
318
8875
    (16)
, then subtract both sides of equation (16) from both sides of equation (6), get the equation：
 350A -250B -3G = 0    (1)
 
500
7
B - 
8
7
G = -1    (2)
 75C -75D -1G = 0    (3)
 60D + 500E -1G = 0    (4)
 
28
3
E -1F - 
1
60
G = 0    (5)
-1F = - 
31
1420
    (6)
 
71
20
G = 
159
20
    (7)

Divide both sides of equation (7) by 213, get the equation：
         
1
60
G = 
53
1420
    (17)
, then add the two sides of equation (17) to both sides of equation (5), get the equation：
 350A -250B -3G = 0    (1)
 
500
7
B - 
8
7
G = -1    (2)
 75C -75D -1G = 0    (3)
 60D + 500E -1G = 0    (4)
 
28
3
E -1F = 
53
1420
    (5)
-1F = - 
31
1420
    (6)
 
71
20
G = 
159
20
    (7)

Multiply both sides of equation (7) by 20
Divide both sides of equation (7) by 71, get the equation：
         G = 
159
71
    (18)
, then add the two sides of equation (18) to both sides of equation (4), get the equation：
 350A -250B -3G = 0    (1)
 
500
7
B - 
8
7
G = -1    (2)
 75C -75D -1G = 0    (3)
 60D + 500E = 
159
71
    (4)
 
28
3
E -1F = 
53
1420
    (5)
-1F = - 
31
1420
    (6)
 
71
20
G = 
159
20
    (7)

Multiply both sides of equation (7) by 20
Divide both sides of equation (7) by 71, get the equation：
         G = 
159
71
    (19)
, then add the two sides of equation (19) to both sides of equation (3), get the equation：
 350A -250B -3G = 0    (1)
 
500
7
B - 
8
7
G = -1    (2)
 75C -75D = 
159
71
    (3)
 60D + 500E = 
159
71
    (4)
 
28
3
E -1F = 
53
1420
    (5)
-1F = - 
31
1420
    (6)
 
71
20
G = 
159
20
    (7)

Multiply both sides of equation (7) by 160
Divide both sides of equation (7) by 497, get the equation：
         
8
7
G = 
1272
497
    (20)
, then add the two sides of equation (20) to both sides of equation (2), get the equation：
 350A -250B -3G = 0    (1)
 
500
7
B = 
775
497
    (2)
 75C -75D = 
159
71
    (3)
 60D + 500E = 
159
71
    (4)
 
28
3
E -1F = 
53
1420
    (5)
-1F = - 
31
1420
    (6)
 
71
20
G = 
159
20
    (7)

Multiply both sides of equation (7) by 60
Divide both sides of equation (7) by 71, get the equation：
         3G = 
477
71
    (21)
, then add the two sides of equation (21) to both sides of equation (1), get the equation：
 350A -250B = 
477
71
    (1)
 
500
7
B = 
775
497
    (2)
 75C -75D = 
159
71
    (3)
 60D + 500E = 
159
71
    (4)
 
28
3
E -1F = 
53
1420
    (5)
-1F = - 
31
1420
    (6)
 
71
20
G = 
159
20
    (7)

Subtract both sides of equation (6) from both sides of equation (5), get the equation：
 350A -250B = 
477
71
    (1)
 
500
7
B = 
775
497
    (2)
 75C -75D = 
159
71
    (3)
 60D + 500E = 
159
71
    (4)
 
28
3
E = 
21
355
    (5)
-1F = - 
31
1420
    (6)
 G = 
159
71
    (7)

Multiply both sides of equation (5) by 375
Divide both sides of equation (5) by 7, get the equation：
         500E = 
225
71
    (22)
, then subtract both sides of equation (22) from both sides of equation (4), get the equation：
 350A -250B = 
477
71
    (1)
 
500
7
B = 
775
497
    (2)
 75C -75D = 
159
71
    (3)
 60D = - 
66
71
    (4)
 
28
3
E = 
21
355
    (5)
 F = 
31
1420
    (6)
 G = 
159
71
    (7)

Multiply both sides of equation (4) by 5
Divide both sides of equation (4) by 4, get the equation：
         75D = - 
165
142
    (23)
, then add the two sides of equation (23) to both sides of equation (3), get the equation：
 350A -250B = 
477
71
    (1)
 
500
7
B = 
775
497
    (2)
 75C = 
153
142
    (3)
 60D = - 
66
71
    (4)
 E = 
9
1420
    (5)
 F = 
31
1420
    (6)
 G = 
159
71
    (7)

Multiply both sides of equation (2) by 7
Divide both sides of equation (2) by 2, get the equation：
         250B = 
775
142
    (24)
, then add the two sides of equation (24) to both sides of equation (1), get the equation：
 350A = 
1729
142
    (1)
 
500
7
B = 
775
497
    (2)
 C = 
51
3550
    (3)
 D = - 
11
710
    (4)
 E = 
9
1420
    (5)
 F = 
31
1420
    (6)
 G = 
159
71
    (7)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
247
7100
    (1)
 B = 
31
1420
    (2)
 C = 
51
3550
    (3)
 D = - 
11
710
    (4)
 E = 
9
1420
    (5)
 F = 
31
1420
    (6)
 G = 
159
71
    (7)


Therefore, the solution of the equation set is:
A = 
247
7100
B = 
31
1420
C = 
51
3550
D = - 
11
710
E = 
9
1420
F = 
31
1420
G = 
159
71


Convert the solution of the equation set to decimals:
A = 0.034789
B = 0.021831
C = 0.014366
D = -0.015493
E = 0.006338
F = 0.021831
G = 2.239437

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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