Mathematics
         
语言：中文    Language:English
                                Equations   
Fold
                                Unary equation
                                Multivariate equation
                                Math OP  
Unfold
                                Linear algebra      
Unfold
                                Derivative function
                                Function image
                                Hot issues
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:
 20x -10y -18z = -40    (1)
-10x + 24y + 20z = -20    (2)
-18x + 20y + 36z = 0    (3)
Question solving process:

Divide the two sides of equation (1) by 2, the equation can be obtained:
         10x -5y -9z = -20    (4)
, then add the two sides of equation (4) to both sides of equation (2), the equations are reduced to:
 20x -10y -18z = -40    (1)
 19y + 11z = -40    (2)
-18x + 20y + 36z = 0    (3)

Multiply both sides of equation (1) by 9
Divide the two sides of equation (1) by 10, the equation can be obtained:
         18x -9y - 
81
5
z = -36    (5)
, then add the two sides of equation (5) to both sides of equation (3), the equations are reduced to:
 20x -10y -18z = -40    (1)
 19y + 11z = -40    (2)
 11y + 
99
5
z = -36    (3)

Multiply both sides of equation (2) by 11
Divide the two sides of equation (2) by 19, the equation can be obtained:
         11y + 
121
19
z = - 
440
19
    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 20x -10y -18z = -40    (1)
 19y + 11z = -40    (2)
 
1276
95
z = - 
244
19
    (3)

Multiply both sides of equation (3) by 95
Divide both sides of equation (3) by 116, get the equation：
         11z = - 
305
29
    (7)
, then subtract both sides of equation (7) from both sides of equation (2), get the equation：
 20x -10y -18z = -40    (1)
 19y = - 
855
29
    (2)
 
1276
95
z = - 
244
19
    (3)

Multiply both sides of equation (3) by 855
Divide both sides of equation (3) by 638, get the equation：
         18z = - 
5490
319
    (8)
, then add the two sides of equation (8) to both sides of equation (1), get the equation：
 20x -10y = - 
18250
319
    (1)
 19y = - 
855
29
    (2)
 
1276
95
z = - 
244
19
    (3)

Multiply both sides of equation (2) by 10
Divide both sides of equation (2) by 19, get the equation：
         10y = - 
450
29
    (9)
, then add the two sides of equation (9) to both sides of equation (1), get the equation：
 20x = - 
23200
319
    (1)
 19y = - 
855
29
    (2)
 z = - 
305
319
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = - 
1160
319
    (1)
 y = - 
45
29
    (2)
 z = - 
305
319
    (3)


Therefore, the solution of the equation set is:
x = - 
1160
319
y = - 
45
29
z = - 
305
319


Convert the solution of the equation set to decimals:
x = -3.636364
y = -1.551724
z = -0.956113

解方程组的详细方法请参阅：《多元一次方程组的解法》
return