Mathematics
语言：中文
Language:English

current location：Equations > Multivariate equations > Answer
Detailed information：
The input equation set is:
 x + y -1z = 7    (1)
 x -1y + z = 13    (2)
-1x + y + z = 25    (3)
Question solving process:

Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
 x + y -1z = 7    (1)
-2y + 2z = 6    (2)
-1x + y + z = 25    (3)

Add both sides of equation (1) to both sides of equation (3) ,the equations are reduced to:
 x + y -1z = 7    (1)
-2y + 2z = 6    (2)
 2y = 32    (3)

Add both sides of equation (2) to both sides of equation (3) ,the equations are reduced to:
 x + y -1z = 7    (1)
-2y + 2z = 6    (2)
 2z = 38    (3)

Subtract both sides of equation (3) from both sides of equation (2), get the equation：
 x + y -1z = 7    (1)
-2y = -32    (2)
 2z = 38    (3)

Divide both sides of equation (3) by 2, get the equation：
         z = 19    (4)
, then add the two sides of equation (4) to both sides of equation (1), get the equation：
 x + y = 26    (1)
-2y = -32    (2)
 2z = 38    (3)

Divide both sides of equation (2) by 2, get the equation：
        -1y = -16    (5)
, then add the two sides of equation (5) to both sides of equation (1), get the equation：
 x = 10    (1)
-2y = -32    (2)
 z = 19    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = 10    (1)
 y = 16    (2)
 z = 19    (3)


Therefore, the solution of the equation set is:
x = 10
y = 16
z = 19

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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