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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:
 A = 5    (1)
 A + 3B + 9C + 27D = 45    (2)
 4E = 45    (3)
 E + 5F + 25G + 125H = 80    (4)
 B = 0    (5)
 F + 10G + 75H = 0    (6)
 B + 6C + 27D -1F = 0    (7)
 2C + 18D -2G = 0    (8)
Question solving process:

Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
 A = 5    (1)
 3B + 9C + 27D = 40    (2)
 4E = 45    (3)
 E + 5F + 25G + 125H = 80    (4)
 B = 0    (5)
 F + 10G + 75H = 0    (6)
 B + 6C + 27D -1F = 0    (7)
 2C + 18D -2G = 0    (8)

Divide the two sides of equation (2) by 3, the equation can be obtained:
         B + 3C + 9D = 
40
3
    (9)
, then subtract both sides of equation (9) from both sides of equation (5), the equations are reduced to:
 A = 5    (1)
 3B + 9C + 27D = 40    (2)
 4E = 45    (3)
 E + 5F + 25G + 125H = 80    (4)
-3C -9D = - 
40
3
    (5)
 F + 10G + 75H = 0    (6)
 B + 6C + 27D -1F = 0    (7)
 2C + 18D -2G = 0    (8)

Divide the two sides of equation (2) by 3, the equation can be obtained:
         B + 3C + 9D = 
40
3
    (10)
, then subtract both sides of equation (10) from both sides of equation (7), the equations are reduced to:
 A = 5    (1)
 3B + 9C + 27D = 40    (2)
 4E = 45    (3)
 E + 5F + 25G + 125H = 80    (4)
-3C -9D = - 
40
3
    (5)
 F + 10G + 75H = 0    (6)
 3C + 18D -1F = - 
40
3
    (7)
 2C + 18D -2G = 0    (8)

交After the exchange of equation (3) and equation (5)， the equation system becomes:
 A = 5    (1)
 3B + 9C + 27D = 40    (2)
-3C -9D = - 
40
3
    (3)
 E + 5F + 25G + 125H = 80    (4)
 4E = 45    (5)
 F + 10G + 75H = 0    (6)
 3C + 18D -1F = - 
40
3
    (7)
 2C + 18D -2G = 0    (8)

Add both sides of equation (3) to both sides of equation (7) ,the equations are reduced to:
 A = 5    (1)
 3B + 9C + 27D = 40    (2)
-3C -9D = - 
40
3
    (3)
 E + 5F + 25G + 125H = 80    (4)
 4E = 45    (5)
 F + 10G + 75H = 0    (6)
 9D -1F = - 
80
3
    (7)
 2C + 18D -2G = 0    (8)

Multiply both sides of equation (3) by 2
Divide the two sides of equation (3) by 3, the equation can be obtained:
        -2C -6D = - 
80
9
    (11)
, then add the two sides of equation (11) to both sides of equation (8), the equations are reduced to:
 A = 5    (1)
 3B + 9C + 27D = 40    (2)
-3C -9D = - 
40
3
    (3)
 E + 5F + 25G + 125H = 80    (4)
 4E = 45    (5)
 F + 10G + 75H = 0    (6)
 9D -1F = - 
80
3
    (7)
 12D -2G = - 
80
9
    (8)

交After the exchange of equation (4) and equation (7)， the equation system becomes:
 A = 5    (1)
 3B + 9C + 27D = 40    (2)
-3C -9D = - 
40
3
    (3)
 9D -1F = - 
80
3
    (4)
 4E = 45    (5)
 F + 10G + 75H = 0    (6)
 E + 5F + 25G + 125H = 80    (7)
 12D -2G = - 
80
9
    (8)

Multiply both sides of equation (4) by 4
Divide the two sides of equation (4) by 3, the equation can be obtained:
         12D - 
4
3
F = - 
320
9
    (12)
, then subtract both sides of equation (12) from both sides of equation (8), the equations are reduced to:
 A = 5    (1)
 3B + 9C + 27D = 40    (2)
-3C -9D = - 
40
3
    (3)
 9D -1F = - 
80
3
    (4)
 4E = 45    (5)
 F + 10G + 75H = 0    (6)
 E + 5F + 25G + 125H = 80    (7)
 
4
3
F -2G = 
80
3
    (8)

Divide the two sides of equation (5) by 4, the equation can be obtained:
         E = 
45
4
    (13)
, then subtract both sides of equation (13) from both sides of equation (7), the equations are reduced to:
 A = 5    (1)
 3B + 9C + 27D = 40    (2)
-3C -9D = - 
40
3
    (3)
 9D -1F = - 
80
3
    (4)
 4E = 45    (5)
 F + 10G + 75H = 0    (6)
 5F + 25G + 125H = 
275
4
    (7)
 
4
3
F -2G = 
80
3
    (8)

Multiply both sides of equation (6) by 5, the equation can be obtained:
         5F + 50G + 375H = 0    (14)
, then subtract both sides of equation (14) from both sides of equation (7), the equations are reduced to:
 A = 5    (1)
 3B + 9C + 27D = 40    (2)
-3C -9D = - 
40
3
    (3)
 9D -1F = - 
80
3
    (4)
 4E = 45    (5)
 F + 10G + 75H = 0    (6)
-25G -250H = 
275
4
    (7)
 
4
3
F -2G = 
80
3
    (8)

Multiply both sides of equation (6) by 4
Divide the two sides of equation (6) by 3, the equation can be obtained:
         
4
3
F + 
40
3
G + 100H = 0    (15)
, then subtract both sides of equation (15) from both sides of equation (8), the equations are reduced to:
 A = 5    (1)
 3B + 9C + 27D = 40    (2)
-3C -9D = - 
40
3
    (3)
 9D -1F = - 
80
3
    (4)
 4E = 45    (5)
 F + 10G + 75H = 0    (6)
-25G -250H = 
275
4
    (7)
- 
46
3
G -100H = 
80
3
    (8)

Multiply both sides of equation (7) by 46
Divide the two sides of equation (7) by 75, the equation can be obtained:
        - 
46
3
G - 
460
3
H = 
253
6
    (16)
, then subtract both sides of equation (16) from both sides of equation (8), the equations are reduced to:
 A = 5    (1)
 3B + 9C + 27D = 40    (2)
-3C -9D = - 
40
3
    (3)
 9D -1F = - 
80
3
    (4)
 4E = 45    (5)
 F + 10G + 75H = 0    (6)
-25G -250H = 
275
4
    (7)
 
160
3
H = - 
31
2
    (8)

Multiply both sides of equation (8) by 75
Divide both sides of equation (8) by 16, get the equation：
         250H = - 
2325
32
    (17)
, then add the two sides of equation (17) to both sides of equation (7), get the equation：
 A = 5    (1)
 3B + 9C + 27D = 40    (2)
-3C -9D = - 
40
3
    (3)
 9D -1F = - 
80
3
    (4)
 4E = 45    (5)
 F + 10G + 75H = 0    (6)
-25G = - 
125
32
    (7)
 
160
3
H = - 
31
2
    (8)

Multiply both sides of equation (8) by 45
Divide both sides of equation (8) by 32, get the equation：
         75H = - 
1395
64
    (18)
, then subtract both sides of equation (18) from both sides of equation (6), get the equation：
 A = 5    (1)
 3B + 9C + 27D = 40    (2)
-3C -9D = - 
40
3
    (3)
 9D -1F = - 
80
3
    (4)
 4E = 45    (5)
 F + 10G = 
1395
64
    (6)
-25G = - 
125
32
    (7)
 
160
3
H = - 
31
2
    (8)

Multiply both sides of equation (7) by 2
Divide both sides of equation (7) by 5, get the equation：
        -10G = - 
25
16
    (19)
, then add the two sides of equation (19) to both sides of equation (6), get the equation：
 A = 5    (1)
 3B + 9C + 27D = 40    (2)
-3C -9D = - 
40
3
    (3)
 9D -1F = - 
80
3
    (4)
 4E = 45    (5)
 F = 
1295
64
    (6)
-25G = - 
125
32
    (7)
 H = - 
93
320
    (8)

Add both sides of equation (6) to both sides of equation (4), get the equation：
 A = 5    (1)
 3B + 9C + 27D = 40    (2)
-3C -9D = - 
40
3
    (3)
 9D = - 
1235
192
    (4)
 4E = 45    (5)
 F = 
1295
64
    (6)
 G = 
5
32
    (7)
 H = - 
93
320
    (8)

Add both sides of equation (4) to both sides of equation (3), get the equation：
 A = 5    (1)
 3B + 9C + 27D = 40    (2)
-3C = - 
1265
64
    (3)
 9D = - 
1235
192
    (4)
 E = 
45
4
    (5)
 F = 
1295
64
    (6)
 G = 
5
32
    (7)
 H = - 
93
320
    (8)

Multiply both sides of equation (4) by 3, get the equation：
         27D = - 
1235
64
    (20)
, then subtract both sides of equation (20) from both sides of equation (2), get the equation：
 A = 5    (1)
 3B + 9C = 
3795
64
    (2)
-3C = - 
1265
64
    (3)
 9D = - 
1235
192
    (4)
 E = 
45
4
    (5)
 F = 
1295
64
    (6)
 G = 
5
32
    (7)
 H = - 
93
320
    (8)

Multiply both sides of equation (3) by 3, get the equation：
        -9C = - 
3795
64
    (21)
, then add the two sides of equation (21) to both sides of equation (2), get the equation：
 A = 5    (1)
 3B = 0    (2)
-3C = - 
1265
64
    (3)
 D = - 
1235
1728
    (4)
 E = 
45
4
    (5)
 F = 
1295
64
    (6)
 G = 
5
32
    (7)
 H = - 
93
320
    (8)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 5    (1)
 B = 0    (2)
 C = 
1265
192
    (3)
 D = - 
1235
1728
    (4)
 E = 
45
4
    (5)
 F = 
1295
64
    (6)
 G = 
5
32
    (7)
 H = - 
93
320
    (8)


Therefore, the solution of the equation set is:
A = 5
B = 0
C = 
1265
192
D = - 
1235
1728
E = 
45
4
F = 
1295
64
G = 
5
32
H = - 
93
320


Convert the solution of the equation set to decimals:
A = 5
B = 0
C = 6.588542
D = -0.714699
E = 11.250000
F = 20.234375
G = 0.156250
H = -0.290625

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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