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:
 10x + 5y + 20z = 
1146789
50
    (1)
 17x + 5y + 6z = 
2762431
100
    (2)
 13x + 5y + 8z = 
2631571
100
    (3)
Question solving process:

Multiply both sides of equation (1) by 17
Divide the two sides of equation (1) by 10, the equation can be obtained:
         17x + 
17
2
y + 34z = 
19495413
500
    (4)
, then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
 10x + 5y + 20z = 
1146789
50
    (1)
7
2
y -28z = 
2841629
250
    (2)
 13x + 5y + 8z = 
2631571
100
    (3)

Multiply both sides of equation (1) by 13
Divide the two sides of equation (1) by 10, the equation can be obtained:
         13x + 
13
2
y + 26z = 
14908257
500
    (5)
, then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 10x + 5y + 20z = 
1146789
50
    (1)
7
2
y -28z = 
2841629
250
    (2)
3
2
y -18z = 
875201
250
    (3)

Multiply both sides of equation (2) by 3
Divide the two sides of equation (2) by 7, the equation can be obtained:
        
3
2
y -12z = 
1217841
250
    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 10x + 5y + 20z = 
1146789
50
    (1)
7
2
y -28z = 
2841629
250
    (2)
-6z = 
34264
25
    (3)

Multiply both sides of equation (3) by 14
Divide both sides of equation (3) by 3, get the equation:
        -28z = 
479696
75
    (7)
, then subtract both sides of equation (7) from both sides of equation (2), get the equation:
 10x + 5y + 20z = 
1146789
50
    (1)
7
2
y = 
13321847
750
    (2)
-6z = 
34264
25
    (3)

Multiply both sides of equation (3) by 10
Divide both sides of equation (3) by 3, get the equation:
        -20z = 
68528
15
    (8)
, then add the two sides of equation (8) to both sides of equation (1), get the equation:
 10x + 5y = 
4125647
150
    (1)
7
2
y = 
13321847
750
    (2)
-6z = 
34264
25
    (3)

Multiply both sides of equation (2) by 10
Divide both sides of equation (2) by 7, get the equation:
        -5y = 
1903121
75
    (9)
, then add the two sides of equation (9) to both sides of equation (1), get the equation:
 10x = 
63881
30
    (1)
7
2
y = 
13321847
750
    (2)
 z = 
17132
75
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 x = 
63881
300
    (1)
 y = 
1903121
375
    (2)
 z = 
17132
75
    (3)


Therefore, the solution of the equation set is:
x = 
63881
300
y = 
1903121
375
z = 
17132
75


Convert the solution of the equation set to decimals:
x = 212.936667
y = 5074.989333
z = -228.426667

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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