Mathematics
语言：中文
Language:English

current location：Equations > Multivariate equations > Answer
Detailed information：
The input equation set is:
 x + y + z = 120    (1)
 x -1y = 1    (2)
 y -1z = 7    (3)
Question solving process:

Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
 x + y + z = 120    (1)
-2y -1z = -119    (2)
 y -1z = 7    (3)

Divide the two sides of equation (2) by 2, the equation can be obtained:
        -1y - 
1
2
z = - 
119
2
    (4)
, then add the two sides of equation (4) to both sides of equation (3), the equations are reduced to:
 x + y + z = 120    (1)
-2y -1z = -119    (2)
- 
3
2
z = - 
105
2
    (3)

Multiply both sides of equation (3) by 2
Divide both sides of equation (3) by 3, get the equation：
        -1z = -35    (5)
, then subtract both sides of equation (5) from both sides of equation (2), get the equation：
 x + y + z = 120    (1)
-2y = -84    (2)
- 
3
2
z = - 
105
2
    (3)

Multiply both sides of equation (3) by 2
Divide both sides of equation (3) by 3, get the equation：
        -1z = -35    (6)
, then add the two sides of equation (6) to both sides of equation (1), get the equation：
 x + y = 85    (1)
-2y = -84    (2)
- 
3
2
z = - 
105
2
    (3)

Divide both sides of equation (2) by 2, get the equation：
        -1y = -42    (7)
, then add the two sides of equation (7) to both sides of equation (1), get the equation：
 x = 43    (1)
-2y = -84    (2)
 z = 35    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = 43    (1)
 y = 42    (2)
 z = 35    (3)


Therefore, the solution of the equation set is:
x = 43
y = 42
z = 35

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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