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:
 
47
5
A + 
221
5
B + 
107
2
C + 
23
2
D = 
87
5
    (1)
 
2
5
A + 
12
5
B + 
17
5
C + 
2
5
D = 
7
5
    (2)
0 = 0    (3)
0 = 0    (4)
Question solving process:

Multiply both sides of equation (1) by 2
Divide the two sides of equation (1) by 47, the equation can be obtained:
         
2
5
A + 
442
235
B + 
107
47
C + 
23
47
D = 
174
235
    (5)
, then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
 
47
5
A + 
221
5
B + 
107
2
C + 
23
2
D = 
87
5
    (1)
 
122
235
B + 
264
235
C 
21
235
D = 
31
47
    (2)
0 = 0    (3)
0 = 0    (4)

Multiply both sides of equation (2) by 10387
Divide both sides of equation (2) by 122, get the equation:
         
10387
235
B + 
29172
305
C 
4641
610
D = 
6851
122
    (6)
, then subtract both sides of equation (6) from both sides of equation (1), get the equation:
 
47
5
A 
25709
610
C + 
5828
305
D = 
23641
610
    (1)
 
122
235
B + 
264
235
C 
21
235
D = 
31
47
    (2)
0 = 0    (3)
0 = 0    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 A 
547
122
C + 
124
61
D = 
503
122
    (1)
 B + 
132
61
C 
21
122
D = 
155
122
    (2)
0 = 0    (3)
0 = 0    (4)


Therefore, the solution of the equation set is:
A = 
503
122
 + 
547
122
C - 
124
61
D
B = 
155
122
 - 
132
61
C + 
21
122
D


Convert the solution of the equation set to decimals:
A = -4.122951 + 
547
122
C - 
124
61
D
B = 1.270492 - 
132
61
C + 
21
122
D

Where:  C, D are arbitrary constants.
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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