Mathematics
         
语言：中文    Language:English
Equations   
Fold
Unary equation
Multivariate equation
Math OP  
Unfold
Linear algebra      
Unfold
Derivative function
Function image
Hot issues
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:
 A -1G = -136980    (1)
 B -1G = -236312    (2)
 C -1G = -214388    (3)
 D -1G = - 
60923971
2000
    (4)
 E -1G = - 
117865371
2000
    (5)
 F -1G = - 
102725371
2000
    (6)
-2D -1E + 2F = - 
294051371
2000
    (7)
Question solving process:

Multiply both sides of equation (4) by 2, the equation can be obtained:
         2D -2G = - 
60923971
1000
    (8)
, then add the two sides of equation (8) to both sides of equation (7), the equations are reduced to:
 A -1G = -136980    (1)
 B -1G = -236312    (2)
 C -1G = -214388    (3)
 D -1G = - 
60923971
2000
    (4)
 E -1G = - 
117865371
2000
    (5)
 F -1G = - 
102725371
2000
    (6)
-1E + 2F -2G = - 
415899313
2000
    (7)

Add both sides of equation (5) to both sides of equation (7) ,the equations are reduced to:
 A -1G = -136980    (1)
 B -1G = -236312    (2)
 C -1G = -214388    (3)
 D -1G = - 
60923971
2000
    (4)
 E -1G = - 
117865371
2000
    (5)
 F -1G = - 
102725371
2000
    (6)
 2F -3G = - 
133441171
500
    (7)

Multiply both sides of equation (6) by 2, the equation can be obtained:
         2F -2G = - 
102725371
1000
    (9)
, then subtract both sides of equation (9) from both sides of equation (7), the equations are reduced to:
 A -1G = -136980    (1)
 B -1G = -236312    (2)
 C -1G = -214388    (3)
 D -1G = - 
60923971
2000
    (4)
 E -1G = - 
117865371
2000
    (5)
 F -1G = - 
102725371
2000
    (6)
-1G = - 
164156971
1000
    (7)

Subtract both sides of equation (7) from both sides of equation (6), get the equation：
 A -1G = -136980    (1)
 B -1G = -236312    (2)
 C -1G = -214388    (3)
 D -1G = - 
60923971
2000
    (4)
 E -1G = - 
117865371
2000
    (5)
 F = 
225588571
2000
    (6)
-1G = - 
164156971
1000
    (7)

Subtract both sides of equation (7) from both sides of equation (5), get the equation：
 A -1G = -136980    (1)
 B -1G = -236312    (2)
 C -1G = -214388    (3)
 D -1G = - 
60923971
2000
    (4)
 E = 
210448571
2000
    (5)
 F = 
225588571
2000
    (6)
-1G = - 
164156971
1000
    (7)

Subtract both sides of equation (7) from both sides of equation (4), get the equation：
 A -1G = -136980    (1)
 B -1G = -236312    (2)
 C -1G = -214388    (3)
 D = 
267389971
2000
    (4)
 E = 
210448571
2000
    (5)
 F = 
225588571
2000
    (6)
-1G = - 
164156971
1000
    (7)

Subtract both sides of equation (7) from both sides of equation (3), get the equation：
 A -1G = -136980    (1)
 B -1G = -236312    (2)
 C = - 
50231029
1000
    (3)
 D = 
267389971
2000
    (4)
 E = 
210448571
2000
    (5)
 F = 
225588571
2000
    (6)
-1G = - 
164156971
1000
    (7)

Subtract both sides of equation (7) from both sides of equation (2), get the equation：
 A -1G = -136980    (1)
 B = - 
72155029
1000
    (2)
 C = - 
50231029
1000
    (3)
 D = 
267389971
2000
    (4)
 E = 
210448571
2000
    (5)
 F = 
225588571
2000
    (6)
-1G = - 
164156971
1000
    (7)

Subtract both sides of equation (7) from both sides of equation (1), get the equation：
 A = 
27176971
1000
    (1)
 B = - 
72155029
1000
    (2)
 C = - 
50231029
1000
    (3)
 D = 
267389971
2000
    (4)
 E = 
210448571
2000
    (5)
 F = 
225588571
2000
    (6)
-1G = - 
164156971
1000
    (7)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
27176971
1000
    (1)
 B = - 
72155029
1000
    (2)
 C = - 
50231029
1000
    (3)
 D = 
267389971
2000
    (4)
 E = 
210448571
2000
    (5)
 F = 
225588571
2000
    (6)
 G = 
164156971
1000
    (7)


Therefore, the solution of the equation set is:
A = 
27176971
1000
B = - 
72155029
1000
C = - 
50231029
1000
D = 
267389971
2000
E = 
210448571
2000
F = 
225588571
2000
G = 
164156971
1000


Convert the solution of the equation set to decimals:
A = 27176.971000
B = -72155.029000
C = -50231.029000
D = 133694.985500
E = 105224.285500
F = 112794.285500
G = 164156.971000

解方程组的详细方法请参阅：《多元一次方程组的解法》
return







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