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:
 1000000x + 1000y + 100z = -1    (1)
 27000000x + 90000y + 300z = -2    (2)
 148877000x + 280900y + 530z = -2    (3)
Question solving process:

Multiply both sides of equation (1) by 27, the equation can be obtained:
         27000000x + 27000y + 2700z = -27    (4)
, then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
 1000000x + 1000y + 100z = -1    (1)
 63000y -2400z = 25    (2)
 148877000x + 280900y + 530z = -2    (3)

Multiply both sides of equation (1) by 148877
Divide the two sides of equation (1) by 1000, the equation can be obtained:
         148877000x + 148877y + 
148877
10
z = 
148877
1000
    (5)
, then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 1000000x + 1000y + 100z = -1    (1)
 63000y -2400z = 25    (2)
 132023y 
143577
10
z = 
146877
1000
    (3)

Multiply both sides of equation (2) by 132023
Divide the two sides of equation (2) by 63000, the equation can be obtained:
         132023y 
528092
105
z = 
132023
2520
    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 1000000x + 1000y + 100z = -1    (1)
 63000y -2400z = 25    (2)
1958933
210
z = 
1488169
15750
    (3)

Multiply both sides of equation (3) by 504000
Divide both sides of equation (3) by 1958933, get the equation:
        
3856800
1607
z = 
2070496
85171
    (7)
, then subtract both sides of equation (7) from both sides of equation (2), get the equation:
 1000000x + 1000y + 100z = -1    (1)
 63000y = 
58779
85171
    (2)
1958933
210
z = 
1488169
15750
    (3)

Multiply both sides of equation (3) by 21000
Divide both sides of equation (3) by 1958933, get the equation:
        
160700
1607
z = 
258812
255513
    (8)
, then add the two sides of equation (8) to both sides of equation (1), get the equation:
 1000000x + 1000y = 
3299
255513
    (1)
 63000y = 
58779
85171
    (2)
1958933
210
z = 
1488169
15750
    (3)

Divide both sides of equation (2) by 63, get the equation:
         1000y = 
933
85171
    (9)
, then subtract both sides of equation (9) from both sides of equation (1), get the equation:
 1000000x = 
803500
410609391
    (1)
 63000y = 
58779
85171
    (2)
 z = 
64703
6387825
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 x = 
1607
880028464
    (1)
 y = 
933
85171000
    (2)
 z = 
64703
6387825
    (3)


Therefore, the solution of the equation set is:
x = 
1607
880028464
y = 
933
85171000
z = 
64703
6387825


Convert the solution of the equation set to decimals:
x = 0.000002
y = 0.000011
z = -0.010129

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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