当m为何值时，关于x,y的方程组{2x+y=m,x+4y=8 的解是正数①*4-②得7x=4m-8x=(4m-8)/7y=m-2x=

①*4-②得
7x=4m-8
x=(4m-8)/7
y=m-2x=m-2*(4m-8)/7=(16-m)7
所以
x>0且y>0
(4m-8)/7>0且(16-m)7>0
4m-8>0且16-m>0
2所以当2 变式，y=m-2x;带入等式得x+4(m-2x)=8;整理得：x=(4m-8)/7;x要为正数x大于0;解得m>2

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2x+y=m (1)
x+4y=8 (2)
（1)*4-(2),得
x=(4m-8)/7 ```````(3)
(2)*2-(1),得
y=(16-m)/7`````````(4)
又因为x>0,y>0 得
m>2,m<16

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