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:
 711A + 5325B + C = 3030    (1)
 744A + 5325B + C = 3092    (2)
 790A + 5325B + C = 3178    (3)
 832A + 5325B + C = 3257    (4)
 790A + 5734B + C = 3317    (5)
 832A + 5734B + C = 3396    (6)
Question solving process:

Multiply both sides of equation (1) by 248
Divide the two sides of equation (1) by 237, the equation can be obtained:
         744A + 
440200
79
B + 
248
237
C = 
250480
79
    (7)
, then subtract both sides of equation (7) from both sides of equation (2), the equations are reduced to:
 711A + 5325B + C = 3030    (1)
19525
79
B 
11
237
C = 
6212
79
    (2)
 790A + 5325B + C = 3178    (3)
 832A + 5325B + C = 3257    (4)
 790A + 5734B + C = 3317    (5)
 832A + 5734B + C = 3396    (6)

Multiply both sides of equation (1) by 790
Divide the two sides of equation (1) by 711, the equation can be obtained:
         790A + 
1402250
237
B + 
790
711
C = 
797900
237
    (8)
, then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
 711A + 5325B + C = 3030    (1)
19525
79
B 
11
237
C = 
6212
79
    (2)
140225
237
B 
1
9
C = 
44714
237
    (3)
 832A + 5325B + C = 3257    (4)
 790A + 5734B + C = 3317    (5)
 832A + 5734B + C = 3396    (6)

Multiply both sides of equation (1) by 832
Divide the two sides of equation (1) by 711, the equation can be obtained:
         832A + 
1476800
237
B + 
832
711
C = 
840320
237
    (9)
, then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
 711A + 5325B + C = 3030    (1)
19525
79
B 
11
237
C = 
6212
79
    (2)
140225
237
B 
1
9
C = 
44714
237
    (3)
214775
237
B 
121
711
C = 
68411
237
    (4)
 790A + 5734B + C = 3317    (5)
 832A + 5734B + C = 3396    (6)

Multiply both sides of equation (1) by 790
Divide the two sides of equation (1) by 711, the equation can be obtained:
         790A + 
1402250
237
B + 
790
711
C = 
797900
237
    (10)
, then subtract both sides of equation (10) from both sides of equation (5), the equations are reduced to:
 711A + 5325B + C = 3030    (1)
19525
79
B 
11
237
C = 
6212
79
    (2)
140225
237
B 
1
9
C = 
44714
237
    (3)
214775
237
B 
121
711
C = 
68411
237
    (4)
43292
237
B 
1
9
C = 
11771
237
    (5)
 832A + 5734B + C = 3396    (6)

Multiply both sides of equation (1) by 832
Divide the two sides of equation (1) by 711, the equation can be obtained:
         832A + 
1476800
237
B + 
832
711
C = 
840320
237
    (11)
, then subtract both sides of equation (11) from both sides of equation (6), the equations are reduced to:
 711A + 5325B + C = 3030    (1)
19525
79
B 
11
237
C = 
6212
79
    (2)
140225
237
B 
1
9
C = 
44714
237
    (3)
214775
237
B 
121
711
C = 
68411
237
    (4)
43292
237
B 
1
9
C = 
11771
237
    (5)
117842
237
B 
121
711
C = 
35468
237
    (6)

Multiply both sides of equation (2) by 5609
Divide the two sides of equation (2) by 2343, the equation can be obtained:
        
126025
213
B 
1
9
C = 
441052
2343
    (12)
, then subtract both sides of equation (12) from both sides of equation (3), the equations are reduced to:
 711A + 5325B + C = 3030    (1)
19525
79
B 
11
237
C = 
6212
79
    (2)
0 = 
1106
2607
    (3)
214775
237
B 
121
711
C = 
68411
237
    (4)
43292
237
B 
1
9
C = 
11771
237
    (5)
117842
237
B 
121
711
C = 
35468
237
    (6)

由第(3)方程式可以看出,该方程组无解。

解方程组的详细方法请参阅:《多元一次方程组的解法》







  New addition:Lenders ToolBox module(Specific location:Math OP > Lenders ToolBox ),welcome。