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:
 7y + 78z = 5    (1)
 6x + 6z = 88    (2)
 3x + 6y + z = -90    (3)
Question solving process:

交After the exchange of equation (1) and equation (2), the equation system becomes:
 6x + 6z = 88    (1)
 7y + 78z = 5    (2)
 3x + 6y + z = -90    (3)

Divide the two sides of equation (1) by 2, the equation can be obtained:
         3x + 3z = 44    (4)
, then subtract both sides of equation (4) from both sides of equation (3), the equations are reduced to:
 6x + 6z = 88    (1)
 7y + 78z = 5    (2)
 6y -2z = -134    (3)

Multiply both sides of equation (2) by 6
Divide the two sides of equation (2) by 7, the equation can be obtained:
         6y + 
468
7
z = 
30
7
    (5)
, then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 6x + 6z = 88    (1)
 7y + 78z = 5    (2)
482
7
z = 
968
7
    (3)

Multiply both sides of equation (3) by 273
Divide both sides of equation (3) by 241, get the equation:
        
18798
241
z = 
37752
241
    (6)
, then add the two sides of equation (6) to both sides of equation (2), get the equation:
 6x + 6z = 88    (1)
 7y = 
36547
241
    (2)
482
7
z = 
968
7
    (3)

Multiply both sides of equation (3) by 21
Divide both sides of equation (3) by 241, get the equation:
        
1446
241
z = 
2904
241
    (7)
, then add the two sides of equation (7) to both sides of equation (1), get the equation:
 6x = 
18304
241
    (1)
 7y = 
36547
241
    (2)
482
7
z = 
968
7
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 x = 
9152
723
    (1)
 y = 
5221
241
    (2)
 z = 
484
241
    (3)


Therefore, the solution of the equation set is:
x = 
9152
723
y = 
5221
241
z = 
484
241


Convert the solution of the equation set to decimals:
x = 12.658368
y = -21.663900
z = 2.008299

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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