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:
 
12
5
A -5B = 1    (1)
-6A + 6C = 0    (2)
24
5
A + 12D = 0    (3)
1333
500
A + 
2983
50
B 
33
50
C + 
33
50
D = 
218
5
    (4)
Question solving process:

Multiply both sides of equation (1) by 5
Divide the two sides of equation (1) by 2, the equation can be obtained:
         6A 
25
2
B = 
5
2
    (5)
, then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
 
12
5
A -5B = 1    (1)
25
2
B + 6C = 
5
2
    (2)
24
5
A + 12D = 0    (3)
1333
500
A + 
2983
50
B 
33
50
C + 
33
50
D = 
218
5
    (4)

Multiply both sides of equation (1) by 2, the equation can be obtained:
         
24
5
A -10B = 2    (6)
, then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
 
12
5
A -5B = 1    (1)
25
2
B + 6C = 
5
2
    (2)
-10B + 12D = 2    (3)
1333
500
A + 
2983
50
B 
33
50
C + 
33
50
D = 
218
5
    (4)

Multiply both sides of equation (1) by 1333
Divide the two sides of equation (1) by 1200, the equation can be obtained:
         
1333
500
A 
1333
240
B = 
1333
1200
    (7)
, then add the two sides of equation (7) to both sides of equation (4), the equations are reduced to:
 
12
5
A -5B = 1    (1)
25
2
B + 6C = 
5
2
    (2)
-10B + 12D = 2    (3)
 
64927
1200
B 
33
50
C + 
33
50
D = 
53653
1200
    (4)

Multiply both sides of equation (2) by 4
Divide the two sides of equation (2) by 5, the equation can be obtained:
        -10B + 
24
5
C = 2    (8)
, then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
 
12
5
A -5B = 1    (1)
25
2
B + 6C = 
5
2
    (2)
24
5
C + 12D = 0    (3)
 
64927
1200
B 
33
50
C + 
33
50
D = 
53653
1200
    (4)

Multiply both sides of equation (2) by 64927
Divide the two sides of equation (2) by 15000, the equation can be obtained:
        
64927
1200
B + 
64927
2500
C = 
64927
6000
    (9)
, then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
 
12
5
A -5B = 1    (1)
25
2
B + 6C = 
5
2
    (2)
24
5
C + 12D = 0    (3)
 
63277
2500
C + 
33
50
D = 
13883
250
    (4)

Multiply both sides of equation (3) by 63277
Divide the two sides of equation (3) by 12000, the equation can be obtained:
        
63277
2500
C + 
63277
1000
D = 0    (10)
, then add the two sides of equation (10) to both sides of equation (4), the equations are reduced to:
 
12
5
A -5B = 1    (1)
25
2
B + 6C = 
5
2
    (2)
24
5
C + 12D = 0    (3)
 
63937
1000
D = 
13883
250
    (4)

Multiply both sides of equation (4) by 12000
Divide both sides of equation (4) by 63937, get the equation:
         
45132
3761
D = 
666384
63937
    (11)
, then subtract both sides of equation (11) from both sides of equation (3), get the equation:
 
12
5
A -5B = 1    (1)
25
2
B + 6C = 
5
2
    (2)
24
5
C = 
666384
63937
    (3)
 
63937
1000
D = 
13883
250
    (4)

Multiply both sides of equation (3) by 5
Divide both sides of equation (3) by 4, get the equation:
        -6C = 
832980
63937
    (12)
, then add the two sides of equation (12) to both sides of equation (2), get the equation:
 
12
5
A -5B = 1    (1)
25
2
B = 
1346275
127874
    (2)
24
5
C = 
666384
63937
    (3)
 D = 
55532
63937
    (4)

Multiply both sides of equation (2) by 2
Divide both sides of equation (2) by 5, get the equation:
        -5B = 
269255
63937
    (13)
, then subtract both sides of equation (13) from both sides of equation (1), get the equation:
 
12
5
A = 
333192
63937
    (1)
25
2
B = 
1346275
127874
    (2)
 C = 
138830
63937
    (3)
 D = 
55532
63937
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 A = 
138830
63937
    (1)
 B = 
53851
63937
    (2)
 C = 
138830
63937
    (3)
 D = 
55532
63937
    (4)


Therefore, the solution of the equation set is:
A = 
138830
63937
B = 
53851
63937
C = 
138830
63937
D = 
55532
63937


Convert the solution of the equation set to decimals:
A = 2.171356
B = 0.842251
C = 2.171356
D = 0.868542

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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