Mathematics
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Language:English

current location：Equations > Multivariate equations > Answer
Detailed information：
The input equation set is:
 x + y + z = 439    (1)
 x -1z = 112    (2)
 x -1y = 94    (3)
Question solving process:

Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
 x + y + z = 439    (1)
-1y -2z = -327    (2)
 x -1y = 94    (3)

Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:
 x + y + z = 439    (1)
-1y -2z = -327    (2)
-2y -1z = -345    (3)

Multiply both sides of equation (2) by 2, the equation can be obtained:
        -2y -4z = -654    (4)
, then subtract both sides of equation (4) from both sides of equation (3), the equations are reduced to:
 x + y + z = 439    (1)
-1y -2z = -327    (2)
 3z = 309    (3)

Multiply both sides of equation (3) by 2
Divide both sides of equation (3) by 3, get the equation：
         2z = 206    (5)
, then add the two sides of equation (5) to both sides of equation (2), get the equation：
 x + y + z = 439    (1)
-1y = -121    (2)
 3z = 309    (3)

Divide both sides of equation (3) by 3, get the equation：
         z = 103    (6)
, then subtract both sides of equation (6) from both sides of equation (1), get the equation：
 x + y = 336    (1)
-1y = -121    (2)
 3z = 309    (3)

Add both sides of equation (2) to both sides of equation (1), get the equation：
 x = 215    (1)
-1y = -121    (2)
 z = 103    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = 215    (1)
 y = 121    (2)
 z = 103    (3)


Therefore, the solution of the equation set is:
x = 215
y = 121
z = 103

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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