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:
 10x -4y -5z = 0    (1)
-5x -20y + 25z = -50    (2)
-5x + 9y -4z = 0    (3)
Question solving process:

Divide the two sides of equation (1) by 2, the equation can be obtained:
         5x -2y 
5
2
z = 0    (4)
, then add the two sides of equation (4) to both sides of equation (2), the equations are reduced to:
 10x -4y -5z = 0    (1)
-22y + 
45
2
z = -50    (2)
-5x + 9y -4z = 0    (3)

Divide the two sides of equation (1) by 2, the equation can be obtained:
         5x -2y 
5
2
z = 0    (5)
, then add the two sides of equation (5) to both sides of equation (3), the equations are reduced to:
 10x -4y -5z = 0    (1)
-22y + 
45
2
z = -50    (2)
 7y 
13
2
z = 0    (3)

Multiply both sides of equation (2) by 7
Divide the two sides of equation (2) by 22, the equation can be obtained:
        -7y + 
315
44
z = 
175
11
    (6)
, then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
 10x -4y -5z = 0    (1)
-22y + 
45
2
z = -50    (2)
 
29
44
z = 
175
11
    (3)

Multiply both sides of equation (3) by 990
Divide both sides of equation (3) by 29, get the equation:
         
45
2
z = 
15750
29
    (7)
, then subtract both sides of equation (7) from both sides of equation (2), get the equation:
 10x -4y -5z = 0    (1)
-22y = 
14300
29
    (2)
 
29
44
z = 
175
11
    (3)

Multiply both sides of equation (3) by 220
Divide both sides of equation (3) by 29, get the equation:
         5z = 
3500
29
    (8)
, then add the two sides of equation (8) to both sides of equation (1), get the equation:
 10x -4y = 
3500
29
    (1)
-22y = 
14300
29
    (2)
 
29
44
z = 
175
11
    (3)

Multiply both sides of equation (2) by 2
Divide both sides of equation (2) by 11, get the equation:
        -4y = 
2600
29
    (9)
, then subtract both sides of equation (9) from both sides of equation (1), get the equation:
 10x = 
6100
29
    (1)
-22y = 
14300
29
    (2)
 z = 
700
29
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 x = 
610
29
    (1)
 y = 
650
29
    (2)
 z = 
700
29
    (3)


Therefore, the solution of the equation set is:
x = 
610
29
y = 
650
29
z = 
700
29


Convert the solution of the equation set to decimals:
x = -21.034483
y = -22.413793
z = -24.137931

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。