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:
 x + y -1z = 0    (1)
 1510x + 200z = 5    (2)
 1510y + 200z = 12    (3)
Question solving process:

Multiply both sides of equation (1) by 1510, the equation can be obtained:
         1510x + 1510y -1510z = 0    (4)
, then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
 x + y -1z = 0    (1)
-1510y + 1710z = 5    (2)
 1510y + 200z = 12    (3)

Add both sides of equation (2) to both sides of equation (3) ,the equations are reduced to:
 x + y -1z = 0    (1)
-1510y + 1710z = 5    (2)
 
288410
151
z = 
2567
151
    (3)

Multiply both sides of equation (3) by 25821
Divide both sides of equation (3) by 28841, get the equation:
         
326610
191
z = 
2907
191
    (5)
, then subtract both sides of equation (5) from both sides of equation (2), get the equation:
 x + y -1z = 0    (1)
-1510y = 
1952
191
    (2)
 
288410
151
z = 
2567
151
    (3)

Multiply both sides of equation (3) by 151
Divide both sides of equation (3) by 288410, get the equation:
         z = 
2567
288410
    (6)
, then add the two sides of equation (6) to both sides of equation (1), get the equation:
 x + y = 
2567
288410
    (1)
-1510y = 
1952
191
    (2)
 
288410
151
z = 
2567
151
    (3)

Divide both sides of equation (2) by 1510, get the equation:
        
151
151
y = 
976
144205
    (7)
, then add the two sides of equation (7) to both sides of equation (1), get the equation:
 x = 
23493
11017262
    (1)
-1510y = 
1952
191
    (2)
 z = 
2567
288410
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 x = 
23493
11017262
    (1)
 y = 
976
144205
    (2)
 z = 
2567
288410
    (3)


Therefore, the solution of the equation set is:
x = 
23493
11017262
y = 
976
144205
z = 
2567
288410


Convert the solution of the equation set to decimals:
x = 0.002132
y = 0.006768
z = 0.008901

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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