Question

1<x+y<3,-2<x-2y<4,求x,y的取值范围

题目是这样的:
已知-1〈 x + y〈 3 ,且 2〈 x - y〈 4 ,则 2x+3y的取值范围是什么?

Answer 1

设2x+3y=a(x+y)+b(x-y)
a+b=2
a-b=3
a=5/2 b=-1/2
2x+3y=5/2(x+y)-1/2(x-y)
x+y=3 且 2=x-y
时最大2x+3y=13/2
x+y=-1 且 4=x-y
时最小2x+3y=-9/2
-9/2