Mathematics
         
语言:中文    Language:English
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:
 8A + 4D = 1146    (1)
 32B + 5D = 5260    (2)
 34C + 7D = 4450    (3)
 9A + 9B + 9C + 33D = 8000    (4)
Question solving process:

Multiply both sides of equation (1) by 9
Divide the two sides of equation (1) by 8, the equation can be obtained:
         9A + 
9
2
D = 
5157
4
    (5)
, then subtract both sides of equation (5) from both sides of equation (4), the equations are reduced to:
 8A + 4D = 1146    (1)
 32B + 5D = 5260    (2)
 34C + 7D = 4450    (3)
 9B + 9C + 
57
2
D = 
26843
4
    (4)

Multiply both sides of equation (2) by 9
Divide the two sides of equation (2) by 32, the equation can be obtained:
         9B + 
45
32
D = 
11835
8
    (6)
, then subtract both sides of equation (6) from both sides of equation (4), the equations are reduced to:
 8A + 4D = 1146    (1)
 32B + 5D = 5260    (2)
 34C + 7D = 4450    (3)
 9C + 
867
32
D = 
41851
8
    (4)

Multiply both sides of equation (3) by 9
Divide the two sides of equation (3) by 34, the equation can be obtained:
         9C + 
63
34
D = 
20025
17
    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 8A + 4D = 1146    (1)
 32B + 5D = 5260    (2)
 34C + 7D = 4450    (3)
 
13731
544
D = 
551267
136
    (4)

Multiply both sides of equation (4) by 3808
Divide both sides of equation (4) by 13731, get the equation:
         
1393
199
D = 
15435476
13731
    (8)
, then subtract both sides of equation (8) from both sides of equation (3), get the equation:
 8A + 4D = 1146    (1)
 32B + 5D = 5260    (2)
 34C = 
45667474
13731
    (3)
 
13731
544
D = 
551267
136
    (4)

Multiply both sides of equation (4) by 2720
Divide both sides of equation (4) by 13731, get the equation:
         
995
199
D = 
11025340
13731
    (9)
, then subtract both sides of equation (9) from both sides of equation (2), get the equation:
 8A + 4D = 1146    (1)
 32B = 
61199720
13731
    (2)
 34C = 
45667474
13731
    (3)
 
13731
544
D = 
551267
136
    (4)

Multiply both sides of equation (4) by 2176
Divide both sides of equation (4) by 13731, get the equation:
         
796
199
D = 
8820272
13731
    (10)
, then subtract both sides of equation (10) from both sides of equation (1), get the equation:
 8A = 
6915454
13731
    (1)
 32B = 
61199720
13731
    (2)
 34C = 
45667474
13731
    (3)
 
13731
544
D = 
551267
136
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 A = 
3457727
54924
    (1)
 B = 
7649965
54924
    (2)
 C = 
1343161
13731
    (3)
 D = 
2205068
13731
    (4)


Therefore, the solution of the equation set is:
A = 
3457727
54924
B = 
7649965
54924
C = 
1343161
13731
D = 
2205068
13731


Convert the solution of the equation set to decimals:
A = 62.954756
B = 139.282736
C = 97.819605
D = 160.590489

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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