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:
-25x -9y -27z = 0    (1)
 546x + 180y + 537z = 1    (2)
 154x + 50y + 149z = 0    (3)
Question solving process:

Multiply both sides of equation (1) by 546
Divide the two sides of equation (1) by 25, the equation can be obtained:
        -546x 
4914
25
y 
14742
25
z = 0    (4)
, then add the two sides of equation (4) to both sides of equation (2), the equations are reduced to:
-25x -9y -27z = 0    (1)
414
25
y 
1317
25
z = 1    (2)
 154x + 50y + 149z = 0    (3)

Multiply both sides of equation (1) by 154
Divide the two sides of equation (1) by 25, the equation can be obtained:
        -154x 
1386
25
y 
4158
25
z = 0    (5)
, then add the two sides of equation (5) to both sides of equation (3), the equations are reduced to:
-25x -9y -27z = 0    (1)
414
25
y 
1317
25
z = 1    (2)
136
25
y 
433
25
z = 0    (3)

Multiply both sides of equation (2) by 68
Divide the two sides of equation (2) by 207, the equation can be obtained:
        
136
25
y 
29852
1725
z = 
68
207
    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
-25x -9y -27z = 0    (1)
414
25
y 
1317
25
z = 1    (2)
1
69
z = 
68
207
    (3)

Multiply both sides of equation (3) by 90873
Divide both sides of equation (3) by 25, get the equation:
        
1317
25
z = 
29852
25
    (7)
, then subtract both sides of equation (7) from both sides of equation (2), get the equation:
-25x -9y -27z = 0    (1)
414
25
y = 
29877
25
    (2)
1
69
z = 
68
207
    (3)

Multiply both sides of equation (3) by 1863, get the equation:
        -27z = -612    (8)
, then subtract both sides of equation (8) from both sides of equation (1), get the equation:
-25x -9y = 612    (1)
414
25
y = 
29877
25
    (2)
1
69
z = 
68
207
    (3)

Multiply both sides of equation (2) by 25
Divide both sides of equation (2) by 46, get the equation:
        -9y = 
1299
2
    (9)
, then subtract both sides of equation (9) from both sides of equation (1), get the equation:
-25x = 
75
2
    (1)
414
25
y = 
29877
25
    (2)
 z = 
68
3
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 x = 
3
2
    (1)
 y = 
9959
138
    (2)
 z = 
68
3
    (3)


Therefore, the solution of the equation set is:
x = 
3
2
y = 
9959
138
z = 
68
3


Convert the solution of the equation set to decimals:
x = 1.500000
y = -72.166667
z = 22.666667

解方程组的详细方法请参阅:《多元一次方程组的解法》







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