Mathematics
语言：中文
Language:English

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

Multiply both sides of equation (1) by 2, the equation can be obtained:
         2x + 2y + 2z = 4    (4)
, then subtract both sides of equation (4) from both sides of equation (3), the equations are reduced to:
 x + y + z = 2    (1)
 2y -3z = 1    (2)
-3y + z = -5    (3)

Multiply both sides of equation (2) by 3
Divide the two sides of equation (2) by 2, the equation can be obtained:
         3y - 
9
2
z = 
3
2
    (5)
, then add the two sides of equation (5) to both sides of equation (3), the equations are reduced to:
 x + y + z = 2    (1)
 2y -3z = 1    (2)
- 
7
2
z = - 
7
2
    (3)

Multiply both sides of equation (3) by 6
Divide both sides of equation (3) by 7, get the equation：
        -3z = -3    (6)
, then subtract both sides of equation (6) from both sides of equation (2), get the equation：
 x + y + z = 2    (1)
 2y = 4    (2)
- 
7
2
z = - 
7
2
    (3)

Multiply both sides of equation (3) by 2
Divide both sides of equation (3) by 7, get the equation：
        -1z = -1    (7)
, then add the two sides of equation (7) to both sides of equation (1), get the equation：
 x + y = 1    (1)
 2y = 4    (2)
- 
7
2
z = - 
7
2
    (3)

Divide both sides of equation (2) by 2, get the equation：
         y = 2    (8)
, then subtract both sides of equation (8) from both sides of equation (1), get the equation：
 x = -1    (1)
 2y = 4    (2)
 z = 1    (3)

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


Therefore, the solution of the equation set is:
x = -1
y = 2
z = 1

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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