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:
 30A + 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 3
Divide the two sides of equation (1) by 10, the equation can be obtained:
         9A + 
6
5
D = 
1719
5
    (5)
, then subtract both sides of equation (5) from both sides of equation (4), the equations are reduced to:
 30A + 4D = 1146    (1)
 32B + 5D = 5260    (2)
 34C + 7D = 4450    (3)
 9B + 9C + 
159
5
D = 
38281
5
    (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:
 30A + 4D = 1146    (1)
 32B + 5D = 5260    (2)
 34C + 7D = 4450    (3)
 9C + 
4863
160
D = 
247073
40
    (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:
 30A + 4D = 1146    (1)
 32B + 5D = 5260    (2)
 34C + 7D = 4450    (3)
 
77631
2720
D = 
3399241
680
    (4)

Multiply both sides of equation (4) by 19040
Divide both sides of equation (4) by 77631, get the equation:
         
1603
229
D = 
95178748
77631
    (8)
, then subtract both sides of equation (8) from both sides of equation (3), get the equation:
 30A + 4D = 1146    (1)
 32B + 5D = 5260    (2)
 34C = 
250279202
77631
    (3)
 
77631
2720
D = 
3399241
680
    (4)

Multiply both sides of equation (4) by 13600
Divide both sides of equation (4) by 77631, get the equation:
         
1145
229
D = 
67984820
77631
    (9)
, then subtract both sides of equation (9) from both sides of equation (2), get the equation:
 30A + 4D = 1146    (1)
 32B = 
340354240
77631
    (2)
 34C = 
250279202
77631
    (3)
 
77631
2720
D = 
3399241
680
    (4)

Multiply both sides of equation (4) by 10880
Divide both sides of equation (4) by 77631, get the equation:
         
916
229
D = 
54387856
77631
    (10)
, then subtract both sides of equation (10) from both sides of equation (1), get the equation:
 30A = 
34577270
77631
    (1)
 32B = 
340354240
77631
    (2)
 34C = 
250279202
77631
    (3)
 
77631
2720
D = 
3399241
680
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 A = 
3457727
232893
    (1)
 B = 
10636070
77631
    (2)
 C = 
7361153
77631
    (3)
 D = 
13596964
77631
    (4)


Therefore, the solution of the equation set is:
A = 
3457727
232893
B = 
10636070
77631
C = 
7361153
77631
D = 
13596964
77631


Convert the solution of the equation set to decimals:
A = 14.846848
B = 137.008025
C = 94.822339
D = 175.148639

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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