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 + B = 3    (1)
 2A + 8B + C = 1    (2)
 3A + 27B + 8C + D = 2    (3)
 4A + 64B + 27C + 8D + E = 5    (4)
 24B + 18C + 12D + 6E = 0    (5)
Question solving process:

Multiply both sides of equation (1) by 2, the equation can be obtained:
         2A + 2B = 6    (6)
, then subtract both sides of equation (6) from both sides of equation (2), the equations are reduced to:
 A + B = 3    (1)
 6B + C = -5    (2)
 3A + 27B + 8C + D = 2    (3)
 4A + 64B + 27C + 8D + E = 5    (4)
 24B + 18C + 12D + 6E = 0    (5)

Multiply both sides of equation (1) by 3, the equation can be obtained:
         3A + 3B = 9    (7)
, then subtract both sides of equation (7) from both sides of equation (3), the equations are reduced to:
 A + B = 3    (1)
 6B + C = -5    (2)
 24B + 8C + D = -7    (3)
 4A + 64B + 27C + 8D + E = 5    (4)
 24B + 18C + 12D + 6E = 0    (5)

Multiply both sides of equation (1) by 4, the equation can be obtained:
         4A + 4B = 12    (8)
, then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
 A + B = 3    (1)
 6B + C = -5    (2)
 24B + 8C + D = -7    (3)
 60B + 27C + 8D + E = -7    (4)
 24B + 18C + 12D + 6E = 0    (5)

Multiply both sides of equation (2) by 4, the equation can be obtained:
         24B + 4C = -20    (9)
, then subtract both sides of equation (9) from both sides of equation (3), the equations are reduced to:
 A + B = 3    (1)
 6B + C = -5    (2)
 4C + D = 13    (3)
 60B + 27C + 8D + E = -7    (4)
 24B + 18C + 12D + 6E = 0    (5)

Multiply both sides of equation (2) by 10, the equation can be obtained:
         60B + 10C = -50    (10)
, then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
 A + B = 3    (1)
 6B + C = -5    (2)
 4C + D = 13    (3)
 17C + 8D + E = 43    (4)
 24B + 18C + 12D + 6E = 0    (5)

Multiply both sides of equation (2) by 4, the equation can be obtained:
         24B + 4C = -20    (11)
, then subtract both sides of equation (11) from both sides of equation (5), the equations are reduced to:
 A + B = 3    (1)
 6B + C = -5    (2)
 4C + D = 13    (3)
 17C + 8D + E = 43    (4)
 14C + 12D + 6E = 20    (5)

Multiply both sides of equation (3) by 17
Divide the two sides of equation (3) by 4, the equation can be obtained:
         17C + 
17
4
D = 
221
4
    (12)
, then subtract both sides of equation (12) from both sides of equation (4), the equations are reduced to:
 A + B = 3    (1)
 6B + C = -5    (2)
 4C + D = 13    (3)
 
15
4
D + E = - 
49
4
    (4)
 14C + 12D + 6E = 20    (5)

Multiply both sides of equation (3) by 7
Divide the two sides of equation (3) by 2, the equation can be obtained:
         14C + 
7
2
D = 
91
2
    (13)
, then subtract both sides of equation (13) from both sides of equation (5), the equations are reduced to:
 A + B = 3    (1)
 6B + C = -5    (2)
 4C + D = 13    (3)
 
15
4
D + E = - 
49
4
    (4)
 
17
2
D + 6E = - 
51
2
    (5)

Multiply both sides of equation (4) by 34
Divide the two sides of equation (4) by 15, the equation can be obtained:
         
17
2
D + 
34
15
E = - 
833
30
    (14)
, then subtract both sides of equation (14) from both sides of equation (5), the equations are reduced to:
 A + B = 3    (1)
 6B + C = -5    (2)
 4C + D = 13    (3)
 
15
4
D + E = - 
49
4
    (4)
 
56
15
E = 
34
15
    (5)

Multiply both sides of equation (5) by 15
Divide both sides of equation (5) by 56, get the equation：
         E = 
17
28
    (15)
, then subtract both sides of equation (15) from both sides of equation (4), get the equation：
 A + B = 3    (1)
 6B + C = -5    (2)
 4C + D = 13    (3)
 
15
4
D = - 
90
7
    (4)
 
56
15
E = 
34
15
    (5)

Multiply both sides of equation (4) by 4
Divide both sides of equation (4) by 15, get the equation：
         D = - 
24
7
    (16)
, then subtract both sides of equation (16) from both sides of equation (3), get the equation：
 A + B = 3    (1)
 6B + C = -5    (2)
 4C = 
115
7
    (3)
 
15
4
D = - 
90
7
    (4)
 E = 
17
28
    (5)

Divide both sides of equation (3) by 4, get the equation：
         C = 
115
28
    (17)
, then subtract both sides of equation (17) from both sides of equation (2), get the equation：
 A + B = 3    (1)
 6B = - 
255
28
    (2)
 4C = 
115
7
    (3)
 D = - 
24
7
    (4)
 E = 
17
28
    (5)

Divide both sides of equation (2) by 6, get the equation：
         B = - 
85
56
    (18)
, then subtract both sides of equation (18) from both sides of equation (1), get the equation：
 A = 
253
56
    (1)
 6B = - 
255
28
    (2)
 C = 
115
28
    (3)
 D = - 
24
7
    (4)
 E = 
17
28
    (5)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
253
56
    (1)
 B = - 
85
56
    (2)
 C = 
115
28
    (3)
 D = - 
24
7
    (4)
 E = 
17
28
    (5)


Therefore, the solution of the equation set is:
A = 
253
56
B = - 
85
56
C = 
115
28
D = - 
24
7
E = 
17
28


Convert the solution of the equation set to decimals:
A = 4.517857
B = -1.517857
C = 4.107143
D = -3.428571
E = 0.607143

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。