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:
 158000A + 739417B + 459000C + 438000D + 50000E + 275000F = 28232    (1)
 158000A + 781537B + 459000C + 438000D + 50000E + 275000F = 28867    (2)
 285000A + 1934379B + 549000C + 438000D + 50000E + 275000F = 47944    (3)
 158000A + 1327909B + 459000C + 438000D + 50000E + 275000F = 37095    (4)
 158000A + 1330509B + 459000C + 438000D + 50000E + 275000F = 37134    (5)
 158000A + 1327909B + 459000C + 438000D + 50000E + 275000F = 37095    (6)
Question solving process:

Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
 158000A + 739417B + 459000C + 438000D + 50000E + 275000F = 28232    (1)
 42120B = 635    (2)
 285000A + 1934379B + 549000C + 438000D + 50000E + 275000F = 47944    (3)
 158000A + 1327909B + 459000C + 438000D + 50000E + 275000F = 37095    (4)
 158000A + 1330509B + 459000C + 438000D + 50000E + 275000F = 37134    (5)
 158000A + 1327909B + 459000C + 438000D + 50000E + 275000F = 37095    (6)

Multiply both sides of equation (1) by 285
Divide the two sides of equation (1) by 158, the equation can be obtained:
         285000A + 
210733845
158
B + 
65407500
79
C + 
62415000
79
D + 
7125000
79
E + 
39187500
79
F = 
4023060
79
    (7)
, then subtract both sides of equation (7) from both sides of equation (3), the equations are reduced to:
 158000A + 739417B + 459000C + 438000D + 50000E + 275000F = 28232    (1)
 42120B = 635    (2)
 
94898037
158
B 
22036500
79
C 
27813000
79
D 
3175000
79
E 
17462500
79
F = 
235484
79
    (3)
 158000A + 1327909B + 459000C + 438000D + 50000E + 275000F = 37095    (4)
 158000A + 1330509B + 459000C + 438000D + 50000E + 275000F = 37134    (5)
 158000A + 1327909B + 459000C + 438000D + 50000E + 275000F = 37095    (6)

Subtract both sides of equation (1) from both sides of equation (4) ,the equations are reduced to:
 158000A + 739417B + 459000C + 438000D + 50000E + 275000F = 28232    (1)
 42120B = 635    (2)
 
94898037
158
B 
22036500
79
C 
27813000
79
D 
3175000
79
E 
17462500
79
F = 
235484
79
    (3)
 588492B = 8863    (4)
 158000A + 1330509B + 459000C + 438000D + 50000E + 275000F = 37134    (5)
 158000A + 1327909B + 459000C + 438000D + 50000E + 275000F = 37095    (6)

Subtract both sides of equation (1) from both sides of equation (5) ,the equations are reduced to:
 158000A + 739417B + 459000C + 438000D + 50000E + 275000F = 28232    (1)
 42120B = 635    (2)
 
94898037
158
B 
22036500
79
C 
27813000
79
D 
3175000
79
E 
17462500
79
F = 
235484
79
    (3)
 588492B = 8863    (4)
 591092B = 8902    (5)
 158000A + 1327909B + 459000C + 438000D + 50000E + 275000F = 37095    (6)

Subtract both sides of equation (1) from both sides of equation (6) ,the equations are reduced to:
 158000A + 739417B + 459000C + 438000D + 50000E + 275000F = 28232    (1)
 42120B = 635    (2)
 
94898037
158
B 
22036500
79
C 
27813000
79
D 
3175000
79
E 
17462500
79
F = 
235484
79
    (3)
 588492B = 8863    (4)
 591092B = 8902    (5)
 588492B = 8863    (6)

Multiply both sides of equation (2) by 2433283
Divide the two sides of equation (2) by 170640, the equation can be obtained:
         
94898037
158
B = 
309026941
34128
    (8)
, then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
 158000A + 739417B + 459000C + 438000D + 50000E + 275000F = 28232    (1)
 42120B = 635    (2)
22137484
10665
C 
42296
135
D 
108245912
10665
E 
6497956
1185
F = 
410756029
34128
    (3)
 588492B = 8863    (4)
 591092B = 8902    (5)
 588492B = 8863    (6)

Multiply both sides of equation (2) by 5449
Divide the two sides of equation (2) by 390, the equation can be obtained:
         588492B = 
692023
78
    (9)
, then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
 158000A + 739417B + 459000C + 438000D + 50000E + 275000F = 28232    (1)
 42120B = 635    (2)
22137484
10665
C 
42296
135
D 
108245912
10665
E 
6497956
1185
F = 
410756029
34128
    (3)
0 = 
709
78
    (4)
 591092B = 8902    (5)
 588492B = 8863    (6)

由第(4)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。