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:
 2x + 7y + 12z = 100    (1)
 3x + 2y + 7z = 100    (2)
 19y + 9z = 100    (3)
Question solving process:

Multiply both sides of equation (1) by 3
Divide the two sides of equation (1) by 2, the equation can be obtained:
         3x + 
21
2
y + 18z = 150    (4)
, then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
 2x + 7y + 12z = 100    (1)
17
2
y -11z = -50    (2)
 19y + 9z = 100    (3)

Multiply both sides of equation (2) by 38
Divide the two sides of equation (2) by 17, the equation can be obtained:
        -19y 
418
17
z = 
1900
17
    (5)
, then add the two sides of equation (5) to both sides of equation (3), the equations are reduced to:
 2x + 7y + 12z = 100    (1)
17
2
y -11z = -50    (2)
265
17
z = 
200
17
    (3)

Multiply both sides of equation (3) by 187
Divide both sides of equation (3) by 265, get the equation:
        -11z = 
440
53
    (6)
, then subtract both sides of equation (6) from both sides of equation (2), get the equation:
 2x + 7y + 12z = 100    (1)
17
2
y = 
2210
53
    (2)
265
17
z = 
200
17
    (3)

Multiply both sides of equation (3) by 204
Divide both sides of equation (3) by 265, get the equation:
        -12z = 
480
53
    (7)
, then add the two sides of equation (7) to both sides of equation (1), get the equation:
 2x + 7y = 
4820
53
    (1)
17
2
y = 
2210
53
    (2)
265
17
z = 
200
17
    (3)

Multiply both sides of equation (2) by 14
Divide both sides of equation (2) by 17, get the equation:
        -7y = 
1820
53
    (8)
, then add the two sides of equation (8) to both sides of equation (1), get the equation:
 2x = 
3000
53
    (1)
17
2
y = 
2210
53
    (2)
 z = 
40
53
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 x = 
1500
53
    (1)
 y = 
260
53
    (2)
 z = 
40
53
    (3)


Therefore, the solution of the equation set is:
x = 
1500
53
y = 
260
53
z = 
40
53


Convert the solution of the equation set to decimals:
x = 28.301887
y = 4.905660
z = 0.754717

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。