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 = 
2816901
100
    (2)
 13x + 5y + 8z = 
2525251
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 = 
1352727
125
    (2)
 13x + 5y + 8z = 
2525251
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 = 
1352727
125
    (2)
3
2
y -18z = 
1141001
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 = 
4058181
875
    (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 = 
1352727
125
    (2)
-6z = 
25871
350
    (3)

Multiply both sides of equation (3) by 14
Divide both sides of equation (3) by 3, get the equation:
        -28z = 
25871
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 = 
4187536
375
    (2)
-6z = 
25871
350
    (3)

Multiply both sides of equation (3) by 10
Divide both sides of equation (3) by 3, get the equation:
        -20z = 
25871
105
    (8)
, then add the two sides of equation (8) to both sides of equation (1), get the equation:
 10x + 5y = 
24341279
1050
    (1)
7
2
y = 
4187536
375
    (2)
-6z = 
25871
350
    (3)

Multiply both sides of equation (2) by 10
Divide both sides of equation (2) by 7, get the equation:
        -5y = 
8375072
525
    (9)
, then add the two sides of equation (9) to both sides of equation (1), get the equation:
 10x = 
1518227
210
    (1)
7
2
y = 
4187536
375
    (2)
 z = 
25871
2100
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 x = 
1518227
2100
    (1)
 y = 
8375072
2625
    (2)
 z = 
25871
2100
    (3)


Therefore, the solution of the equation set is:
x = 
1518227
2100
y = 
8375072
2625
z = 
25871
2100


Convert the solution of the equation set to decimals:
x = 722.965238
y = 3190.503619
z = -12.319524

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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