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:
 x + 
6063
20
y + 91z = 
39
100000
    (1)
 x + 
30803
100
y + 94z = 
3
100
    (2)
 x + 
31303
100
y + 98z = 
3
100
    (3)
Question solving process:

Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
 x + 
6063
20
y + 91z = 
39
100000
    (1)
 
122
25
y + 3z = 
2961
100000
    (2)
 x + 
31303
100
y + 98z = 
3
100
    (3)

Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:
 x + 
6063
20
y + 91z = 
39
100000
    (1)
 
122
25
y + 3z = 
2961
100000
    (2)
 
247
25
y + 7z = 
2961
100000
    (3)

Multiply both sides of equation (2) by 247
Divide the two sides of equation (2) by 122, the equation can be obtained:
         
247
25
y + 
741
122
z = 
731367
12200000
    (4)
, then subtract both sides of equation (4) from both sides of equation (3), the equations are reduced to:
 x + 
6063
20
y + 91z = 
39
100000
    (1)
 
122
25
y + 3z = 
2961
100000
    (2)
 
113
122
z = 
2961
97600
    (3)

Multiply both sides of equation (3) by 366
Divide both sides of equation (3) by 113, get the equation:
         
339
113
z = 
8883
90400
    (5)
, then subtract both sides of equation (5) from both sides of equation (2), get the equation:
 x + 
6063
20
y + 91z = 
39
100000
    (1)
 
122
25
y = 
180621
1412500
    (2)
 
113
122
z = 
2961
97600
    (3)

Multiply both sides of equation (3) by 11102
Divide both sides of equation (3) by 113, get the equation:
         
10283
113
z = 
269451
90400
    (6)
, then subtract both sides of equation (6) from both sides of equation (1), get the equation:
 x + 
6063
20
y = 
16842891
5650000
    (1)
 
122
25
y = 
180621
1412500
    (2)
 
113
122
z = 
2961
97600
    (3)

Multiply both sides of equation (2) by 30315
Divide both sides of equation (2) by 488, get the equation:
         
6063
20
y = 
17952543
2260000
    (7)
, then subtract both sides of equation (7) from both sides of equation (1), get the equation:
 x = 
2041726133
1276900000
    (1)
 
122
25
y = 
180621
1412500
    (2)
 z = 
2961
90400
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 x = 
2041726133
1276900000
    (1)
 y = 
2961
113000
    (2)
 z = 
2961
90400
    (3)


Therefore, the solution of the equation set is:
x = 
2041726133
1276900000
 5x + 2y = 342    (1)
 10x + 4y = 2152    (2)
Question solving process:

Multiply both sides of equation (1) by 2, the equation can be obtained:
         10x + 4y = 684    (3)
, then subtract both sides of equation (3) from both sides of equation (2), the equations are reduced to:
 5x + 2y = 342    (1)
0 = 1468    (2)

由第(2)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》
y = 
2961
113000
z = 
2961
90400


Convert the solution of the equation set to decimals:
x = -1.598971
y = 0.026204
z = -0.032754

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。