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:
 225x + 15y + z = 1000    (1)
 1024x + 32y + z = 2000    (2)
 40000x + 200y + z = 10000    (3)
Question solving process:

Multiply both sides of equation (1) by 1024
Divide the two sides of equation (1) by 225, the equation can be obtained:
         1024x + 
1024
15
y + 
1024
225
z = 
40960
9
    (4)
, then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
 225x + 15y + z = 1000    (1)
- 
544
15
y - 
799
225
z = - 
22960
9
    (2)
 40000x + 200y + z = 10000    (3)

Multiply both sides of equation (1) by 1600
Divide the two sides of equation (1) by 9, the equation can be obtained:
         40000x + 
8000
3
y + 
1600
9
z = 
1600000
9
    (5)
, then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 225x + 15y + z = 1000    (1)
- 
544
15
y - 
799
225
z = - 
22960
9
    (2)
- 
7400
3
y - 
1591
9
z = - 
1510000
9
    (3)

Multiply both sides of equation (2) by 4625
Divide the two sides of equation (2) by 68, the equation can be obtained:
        - 
7400
3
y - 
8695
36
z = - 
26547500
153
    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 225x + 15y + z = 1000    (1)
- 
544
15
y - 
799
225
z = - 
22960
9
    (2)
 
259
4
z = 
97500
17
    (3)

Multiply both sides of equation (3) by 3196
Divide both sides of equation (3) by 58275, get the equation：
         
799
225
z = 
244400
777
    (7)
, then add the two sides of equation (7) to both sides of equation (2), get the equation：
 225x + 15y + z = 1000    (1)
- 
544
15
y = - 
5213440
2331
    (2)
 
259
4
z = 
97500
17
    (3)

Multiply both sides of equation (3) by 4
Divide both sides of equation (3) by 259, get the equation：
         z = 
390000
4403
    (8)
, then subtract both sides of equation (8) from both sides of equation (1), get the equation：
 225x + 15y = 
4013000
4403
    (1)
- 
544
15
y = - 
5213440
2331
    (2)
 
259
4
z = 
97500
17
    (3)

Multiply both sides of equation (2) by 225
Divide both sides of equation (2) by 544, get the equation：
        -15y = - 
4073000
4403
    (9)
, then add the two sides of equation (9) to both sides of equation (1), get the equation：
 225x = - 
60000
4403
    (1)
- 
544
15
y = - 
5213440
2331
    (2)
 z = 
390000
4403
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = - 
800
13209
    (1)
 y = 
814600
13209
    (2)
 z = 
390000
4403
    (3)


Therefore, the solution of the equation set is:
x = - 
800
13209
y = 
814600
13209
z = 
390000
4403


Convert the solution of the equation set to decimals:
x = -0.060565
y = 61.670073
z = 88.575971

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。