Mathematics
语言：中文
Language:English

current location：Equations > Multivariate equations > Answer
Detailed information：
The input equation set is:
 x + y + z = 36    (1)
 x -1y = 11    (2)
 y -1z = 5    (3)
Question solving process:

Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
 x + y + z = 36    (1)
-2y -1z = -25    (2)
 y -1z = 5    (3)

Divide the two sides of equation (2) by 2, the equation can be obtained:
        -1y - 
1
2
z = - 
25
2
    (4)
, then add the two sides of equation (4) to both sides of equation (3), the equations are reduced to:
 x + y + z = 36    (1)
-2y -1z = -25    (2)
- 
3
2
z = - 
15
2
    (3)

Multiply both sides of equation (3) by 2
Divide both sides of equation (3) by 3, get the equation：
        -1z = -5    (5)
, then subtract both sides of equation (5) from both sides of equation (2), get the equation：
 x + y + z = 36    (1)
-2y = -20    (2)
- 
3
2
z = - 
15
2
    (3)

Multiply both sides of equation (3) by 2
Divide both sides of equation (3) by 3, get the equation：
        -1z = -5    (6)
, then add the two sides of equation (6) to both sides of equation (1), get the equation：
 x + y = 31    (1)
-2y = -20    (2)
- 
3
2
z = - 
15
2
    (3)

Divide both sides of equation (2) by 2, get the equation：
        -1y = -10    (7)
, then add the two sides of equation (7) to both sides of equation (1), get the equation：
 x = 21    (1)
-2y = -20    (2)
 z = 5    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = 21    (1)
 y = 10    (2)
 z = 5    (3)


Therefore, the solution of the equation set is:
x = 21
y = 10
z = 5

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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