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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 + B + C = 0    (1)
 11A + 10B + 3C + D = 0    (2)
 45A + 36B + 2C + 3D + E = 0    (3)
 81A + 54B + 2D + 3E = 0    (4)
 54A + 27B + 2E = 1    (5)
Question solving process:

Multiply both sides of equation (1) by 11, the equation can be obtained:
         11A + 11B + 11C = 0    (6)
, then subtract both sides of equation (6) from both sides of equation (2), the equations are reduced to:
 A + B + C = 0    (1)
-1B -8C + D = 0    (2)
 45A + 36B + 2C + 3D + E = 0    (3)
 81A + 54B + 2D + 3E = 0    (4)
 54A + 27B + 2E = 1    (5)

Multiply both sides of equation (1) by 45, the equation can be obtained:
         45A + 45B + 45C = 0    (7)
, then subtract both sides of equation (7) from both sides of equation (3), the equations are reduced to:
 A + B + C = 0    (1)
-1B -8C + D = 0    (2)
-9B -43C + 3D + E = 0    (3)
 81A + 54B + 2D + 3E = 0    (4)
 54A + 27B + 2E = 1    (5)

Multiply both sides of equation (1) by 81, the equation can be obtained:
         81A + 81B + 81C = 0    (8)
, then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
 A + B + C = 0    (1)
-1B -8C + D = 0    (2)
-9B -43C + 3D + E = 0    (3)
-27B -81C + 2D + 3E = 0    (4)
 54A + 27B + 2E = 1    (5)

Multiply both sides of equation (1) by 54, the equation can be obtained:
         54A + 54B + 54C = 0    (9)
, then subtract both sides of equation (9) from both sides of equation (5), the equations are reduced to:
 A + B + C = 0    (1)
-1B -8C + D = 0    (2)
-9B -43C + 3D + E = 0    (3)
-27B -81C + 2D + 3E = 0    (4)
-27B -54C + 2E = 1    (5)

Multiply both sides of equation (2) by 9, the equation can be obtained:
        -9B -72C + 9D = 0    (10)
, then subtract both sides of equation (10) from both sides of equation (3), the equations are reduced to:
 A + B + C = 0    (1)
-1B -8C + D = 0    (2)
 29C -6D + E = 0    (3)
-27B -81C + 2D + 3E = 0    (4)
-27B -54C + 2E = 1    (5)

Multiply both sides of equation (2) by 27, the equation can be obtained:
        -27B -216C + 27D = 0    (11)
, then subtract both sides of equation (11) from both sides of equation (4), the equations are reduced to:
 A + B + C = 0    (1)
-1B -8C + D = 0    (2)
 29C -6D + E = 0    (3)
 135C -25D + 3E = 0    (4)
-27B -54C + 2E = 1    (5)

Multiply both sides of equation (2) by 27, the equation can be obtained:
        -27B -216C + 27D = 0    (12)
, then subtract both sides of equation (12) from both sides of equation (5), the equations are reduced to:
 A + B + C = 0    (1)
-1B -8C + D = 0    (2)
 29C -6D + E = 0    (3)
 135C -25D + 3E = 0    (4)
 162C -27D + 2E = 1    (5)

Multiply both sides of equation (3) by 135
Divide the two sides of equation (3) by 29, the equation can be obtained:
         135C - 
810
29
D + 
135
29
E = 0    (13)
, then subtract both sides of equation (13) from both sides of equation (4), the equations are reduced to:
 A + B + C = 0    (1)
-1B -8C + D = 0    (2)
 29C -6D + E = 0    (3)
 
85
29
D - 
48
29
E = 0    (4)
 162C -27D + 2E = 1    (5)

Multiply both sides of equation (3) by 162
Divide the two sides of equation (3) by 29, the equation can be obtained:
         162C - 
972
29
D + 
162
29
E = 0    (14)
, then subtract both sides of equation (14) from both sides of equation (5), the equations are reduced to:
 A + B + C = 0    (1)
-1B -8C + D = 0    (2)
 29C -6D + E = 0    (3)
 
85
29
D - 
48
29
E = 0    (4)
 
189
29
D - 
104
29
E = 1    (5)

Multiply both sides of equation (4) by 189
Divide the two sides of equation (4) by 85, the equation can be obtained:
         
189
29
D - 
9072
2465
E = 0    (15)
, then subtract both sides of equation (15) from both sides of equation (5), the equations are reduced to:
 A + B + C = 0    (1)
-1B -8C + D = 0    (2)
 29C -6D + E = 0    (3)
 
85
29
D - 
48
29
E = 0    (4)
 
232
2465
E = 1    (5)

Multiply both sides of equation (5) by 510
Divide both sides of equation (5) by 29, get the equation：
         
48
29
E = 
510
29
    (16)
, then add the two sides of equation (16) to both sides of equation (4), get the equation：
 A + B + C = 0    (1)
-1B -8C + D = 0    (2)
 29C -6D + E = 0    (3)
 
85
29
D = 
510
29
    (4)
 
232
2465
E = 1    (5)

Multiply both sides of equation (5) by 2465
Divide both sides of equation (5) by 232, get the equation：
         E = 
2465
232
    (17)
, then subtract both sides of equation (17) from both sides of equation (3), get the equation：
 A + B + C = 0    (1)
-1B -8C + D = 0    (2)
 29C -6D = - 
2465
232
    (3)
 
85
29
D = 
510
29
    (4)
 
232
2465
E = 1    (5)

Multiply both sides of equation (4) by 174
Divide both sides of equation (4) by 85, get the equation：
         6D = 36    (18)
, then add the two sides of equation (18) to both sides of equation (3), get the equation：
 A + B + C = 0    (1)
-1B -8C + D = 0    (2)
 29C = 
5887
232
    (3)
 
85
29
D = 
510
29
    (4)
 E = 
2465
232
    (5)

Multiply both sides of equation (4) by 29
Divide both sides of equation (4) by 85, get the equation：
         D = 6    (19)
, then subtract both sides of equation (19) from both sides of equation (2), get the equation：
 A + B + C = 0    (1)
-1B -8C = -6    (2)
 29C = 
5887
232
    (3)
 
85
29
D = 
510
29
    (4)
 E = 
2465
232
    (5)

Multiply both sides of equation (3) by 8
Divide both sides of equation (3) by 29, get the equation：
         8C = 7    (20)
, then add the two sides of equation (20) to both sides of equation (2), get the equation：
 A + B + C = 0    (1)
-1B = 1    (2)
 29C = 
5887
232
    (3)
 D = 6    (4)
 E = 
2465
232
    (5)

Divide both sides of equation (3) by 29, get the equation：
         C = 
203
232
    (21)
, then subtract both sides of equation (21) from both sides of equation (1), get the equation：
 A + B = - 
203
232
    (1)
-1B = 1    (2)
 29C = 
5887
232
    (3)
 D = 6    (4)
 E = 
2465
232
    (5)

Add both sides of equation (2) to both sides of equation (1), get the equation：
 A = 
1
8
    (1)
-1B = 1    (2)
 C = 
203
232
    (3)
 D = 6    (4)
 E = 
2465
232
    (5)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
1
8
    (1)
 B = -1    (2)
 C = 
203
232
    (3)
 D = 6    (4)
 E = 
2465
232
    (5)


Therefore, the solution of the equation set is:
A = 
1
8
B = -1
C = 
203
232
D = 6
E = 
2465
232


Convert the solution of the equation set to decimals:
A = 0.125000
B = -1
C = 0.875000
D = 6
E = 10.625000

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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