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:
 100A + 13D = 9081    (1)
 64B + 10D = 7335    (2)
 68C + 13D = 3667    (3)
 16A + 16B + 16C + 60D = 8443    (4)
Question solving process:

Multiply both sides of equation (1) by 4
Divide the two sides of equation (1) by 25, the equation can be obtained:
         16A + 
52
25
D = 
36324
25
    (5)
, then subtract both sides of equation (5) from both sides of equation (4), the equations are reduced to:
 100A + 13D = 9081    (1)
 64B + 10D = 7335    (2)
 68C + 13D = 3667    (3)
 16B + 16C + 
1448
25
D = 
174751
25
    (4)

Divide the two sides of equation (2) by 4, the equation can be obtained:
         16B + 
5
2
D = 
7335
4
    (6)
, then subtract both sides of equation (6) from both sides of equation (4), the equations are reduced to:
 100A + 13D = 9081    (1)
 64B + 10D = 7335    (2)
 68C + 13D = 3667    (3)
 16C + 
2771
50
D = 
515629
100
    (4)

Multiply both sides of equation (3) by 4
Divide the two sides of equation (3) by 17, the equation can be obtained:
         16C + 
52
17
D = 
14668
17
    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 100A + 13D = 9081    (1)
 64B + 10D = 7335    (2)
 68C + 13D = 3667    (3)
 
44507
850
D = 
7298893
1700
    (4)

Multiply both sides of equation (4) by 11050
Divide both sides of equation (4) by 44507, get the equation:
         
578591
44507
D = 
94885609
89014
    (8)
, then subtract both sides of equation (8) from both sides of equation (3), get the equation:
 100A + 13D = 9081    (1)
 64B + 10D = 7335    (2)
 68C = 
231528729
89014
    (3)
 
44507
850
D = 
7298893
1700
    (4)

Multiply both sides of equation (4) by 8500
Divide both sides of equation (4) by 44507, get the equation:
         
445070
44507
D = 
36494465
44507
    (9)
, then subtract both sides of equation (9) from both sides of equation (2), get the equation:
 100A + 13D = 9081    (1)
 64B = 
289964380
44507
    (2)
 68C = 
231528729
89014
    (3)
 
44507
850
D = 
7298893
1700
    (4)

Multiply both sides of equation (4) by 11050
Divide both sides of equation (4) by 44507, get the equation:
         
578591
44507
D = 
94885609
89014
    (10)
, then subtract both sides of equation (10) from both sides of equation (1), get the equation:
 100A = 
713450525
89014
    (1)
 64B = 
289964380
44507
    (2)
 68C = 
231528729
89014
    (3)
 
44507
850
D = 
7298893
1700
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 A = 
28538021
356056
    (1)
 B = 
72491095
712112
    (2)
 C = 
13619337
356056
    (3)
 D = 
7298893
89014
    (4)


Therefore, the solution of the equation set is:
A = 
28538021
356056
B = 
72491095
712112
C = 
13619337
356056
D = 
7298893
89014


Convert the solution of the equation set to decimals:
A = 80.150372
B = 101.797323
C = 38.250548
D = 81.997135

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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