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:
 
504
5
A + 168B + 3780C + 30D = 208320    (1)
 275A + 
165
2
B + 6000C + 50D = 345575    (2)
 60A + 36B = 20880    (3)
 
2179
5
A + 
573
2
B + 9780C + 80D = 574775    (4)
Question solving process:

Multiply both sides of equation (1) by 1375
Divide the two sides of equation (1) by 504, the equation can be obtained:
         275A + 
1375
3
B + 
20625
2
C + 
6875
84
D = 
1705000
3
    (5)
, then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
 
504
5
A + 168B + 3780C + 30D = 208320    (1)
2255
6
B 
8625
2
C 
2675
84
D = 
668275
3
    (2)
 60A + 36B = 20880    (3)
 
2179
5
A + 
573
2
B + 9780C + 80D = 574775    (4)

Multiply both sides of equation (1) by 25
Divide the two sides of equation (1) by 42, the equation can be obtained:
         60A + 100B + 2250C + 
125
7
D = 124000    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 
504
5
A + 168B + 3780C + 30D = 208320    (1)
2255
6
B 
8625
2
C 
2675
84
D = 
668275
3
    (2)
-64B -2250C 
125
7
D = -103120    (3)
 
2179
5
A + 
573
2
B + 9780C + 80D = 574775    (4)

Multiply both sides of equation (1) by 2179
Divide the two sides of equation (1) by 504, the equation can be obtained:
         
2179
5
A + 
2179
3
B + 
32685
2
C + 
10895
84
D = 
2701960
3
    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 
504
5
A + 168B + 3780C + 30D = 208320    (1)
2255
6
B 
8625
2
C 
2675
84
D = 
668275
3
    (2)
-64B -2250C 
125
7
D = -103120    (3)
2639
6
B 
13125
2
C 
4175
84
D = 
977635
3
    (4)

Multiply both sides of equation (2) by 384
Divide the two sides of equation (2) by 2255, the equation can be obtained:
        -64B 
331200
451
C 
17120
3157
D = 
17107840
451
    (8)
, then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
 
504
5
A + 168B + 3780C + 30D = 208320    (1)
2255
6
B 
8625
2
C 
2675
84
D = 
668275
3
    (2)
683550
451
C 
39255
3157
D = 
29399280
451
    (3)
2639
6
B 
13125
2
C 
4175
84
D = 
977635
3
    (4)

Multiply both sides of equation (2) by 2639
Divide the two sides of equation (2) by 2255, the equation can be obtained:
        
2639
6
B 
4552275
902
C 
201695
5412
D = 
352715545
1353
    (9)
, then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
 
504
5
A + 168B + 3780C + 30D = 208320    (1)
2255
6
B 
8625
2
C 
2675
84
D = 
668275
3
    (2)
683550
451
C 
39255
3157
D = 
29399280
451
    (3)
683550
451
C 
39255
3157
D = 
29399280
451
    (4)

Subtract both sides of equation (3) from both sides of equation (4) ,the equations are reduced to:
 
504
5
A + 168B + 3780C + 30D = 208320    (1)
2255
6
B 
8625
2
C 
2675
84
D = 
668275
3
    (2)
683550
451
C 
39255
3157
D = 
29399280
451
    (3)
0 = 0    (4)

Multiply both sides of equation (3) by 51865
Divide both sides of equation (3) by 18228, get the equation:
        
8625
2
C 
1504775
42532
D = 
281743100
1519
    (10)
, then subtract both sides of equation (10) from both sides of equation (2), get the equation:
 
504
5
A + 168B + 3780C + 30D = 208320    (1)
2255
6
B + 
112750
31899
D = 
169880425
4557
    (2)
683550
451
C 
39255
3157
D = 
29399280
451
    (3)
0 = 0    (4)

Multiply both sides of equation (3) by 2706
Divide both sides of equation (3) by 1085, get the equation:
        -3780C 
47106
1519
D = 
35279136
217
    (11)
, then add the two sides of equation (11) to both sides of equation (1), get the equation:
 
504
5
A + 168B 
1536
1519
D = 
9926304
217
    (1)
2255
6
B + 
112750
31899
D = 
169880425
4557
    (2)
683550
451
C 
39255
3157
D = 
29399280
451
    (3)
0 = 0    (4)

Multiply both sides of equation (2) by 1008
Divide both sides of equation (2) by 2255, get the equation:
        -168B + 
2400
1519
D = 
3616080
217
    (12)
, then add the two sides of equation (12) to both sides of equation (1), get the equation:
 
504
5
A + 
864
1519
D = 
6310224
217
    (1)
2255
6
B + 
112750
31899
D = 
169880425
4557
    (2)
 C + 
2617
318990
D = 
979976
22785
    (3)
0 = 0    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 A + 
60
10633
D = 
438210
1519
    (1)
 B 
100
10633
D = 
150670
1519
    (2)
 C + 
2617
318990
D = 
979976
22785
    (3)
0 = 0    (4)


Therefore, the solution of the equation set is:
A = 
438210
1519
 - 
60
10633
D
B = 
150670
1519
 + 
100
10633
D
C = 
979976
22785
 - 
2617
318990
D


Convert the solution of the equation set to decimals:
A = 288.485846 - 
60
10633
D
B = 99.190257 + 
100
10633
D
C = 43.009699 - 
2617
318990
D

Where:  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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