方程组 ｛5x+8y+12z=100 x+y+z=14

题目

方程组 ｛5x+8y+12z=100 x+y+z=14
方程组
｛5x+8y+12z=100
x+y+z=14

答案

会有无限多组解.
5x + 8y = 100 - 12z
x + y = 14 - z → 5x + 5y = 70 - 5z
3y = 30 - 7z
y = 10 - (7/3)z
x = 4 + (4/3)z = 4(1 + z/3)
若设x = 4n
z = 3n - 3
y = 10 - (7/3)(3n - 3) = 17 - 7n
所以解为：
x = 4n
y = 17 - 7n
z = 3n - 3
n为任意整数