Mathematics
语言：中文
Language:English
current location：Equations > Multivariate equations > Answer
Detailed information：
The input equation set is:
 5x + 4y + 3z = 45    (1)
 x + y + z = 10    (2)
0 = 0    (3)
Question solving process:

Divide the two sides of equation (1) by 5, the equation can be obtained:
         x + 
4
5
y + 
3
5
z = 9    (4)
, then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
 5x + 4y + 3z = 45    (1)
 
1
5
y + 
2
5
z = 1    (2)
0 = 0    (3)

Multiply both sides of equation (2) by 20, get the equation：
         4y + 8z = 20    (5)
, then subtract both sides of equation (5) from both sides of equation (1), get the equation：
 5x -5z = 25    (1)
 
1
5
y + 
2
5
z = 1    (2)
0 = 0    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x -1z = 5    (1)
 y + 2z = 5    (2)
0 = 0    (3)


Therefore, the solution of the equation set is:
x = 5 + 1z
y = 5 - 2z

Where:  z are arbitrary constants.
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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