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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:
 40x -30y -5z = 30    (1)
-30x + 50y -20z = -5    (2)
-5x -20y + 25z = 0    (3)
Question solving process:

Multiply both sides of equation (1) by 3
Divide the two sides of equation (1) by 4, the equation can be obtained:
         30x - 
45
2
y - 
15
4
z = 
45
2
    (4)
, then add the two sides of equation (4) to both sides of equation (2), the equations are reduced to:
 40x -30y -5z = 30    (1)
 
55
2
y - 
95
4
z = 
35
2
    (2)
-5x -20y + 25z = 0    (3)

Divide the two sides of equation (1) by 8, the equation can be obtained:
         5x - 
15
4
y - 
5
8
z = 
15
4
    (5)
, then add the two sides of equation (5) to both sides of equation (3), the equations are reduced to:
 40x -30y -5z = 30    (1)
 
55
2
y - 
95
4
z = 
35
2
    (2)
- 
95
4
y + 
195
8
z = 
15
4
    (3)

Multiply both sides of equation (2) by 19
Divide the two sides of equation (2) by 22, the equation can be obtained:
         
95
4
y - 
1805
88
z = 
665
44
    (6)
, then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
 40x -30y -5z = 30    (1)
 
55
2
y - 
95
4
z = 
35
2
    (2)
 
85
22
z = 
415
22
    (3)

Multiply both sides of equation (3) by 209
Divide both sides of equation (3) by 34, get the equation：
         
95
4
z = 
7885
68
    (7)
, then add the two sides of equation (7) to both sides of equation (2), get the equation：
 40x -30y -5z = 30    (1)
 
55
2
y = 
9075
68
    (2)
 
85
22
z = 
415
22
    (3)

Multiply both sides of equation (3) by 22
Divide both sides of equation (3) by 17, get the equation：
         5z = 
415
17
    (8)
, then add the two sides of equation (8) to both sides of equation (1), get the equation：
 40x -30y = 
925
17
    (1)
 
55
2
y = 
9075
68
    (2)
 
85
22
z = 
415
22
    (3)

Multiply both sides of equation (2) by 12
Divide both sides of equation (2) by 11, get the equation：
         30y = 
2475
17
    (9)
, then add the two sides of equation (9) to both sides of equation (1), get the equation：
 40x = 200    (1)
 
55
2
y = 
9075
68
    (2)
 z = 
83
17
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = 5    (1)
 y = 
165
34
    (2)
 z = 
83
17
    (3)


Therefore, the solution of the equation set is:
x = 5
y = 
165
34
z = 
83
17


Convert the solution of the equation set to decimals:
x = 5
y = 4.852941
z = 4.882353

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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