破鞋区委书记 刘红霞:已知方程组5x-7y=5m+4和2x-y=3-m的解x,y的和不小于4,求m的范围。(要求有过程)

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5x-7y=5m+4 -> 10x-14y=10m+8 (1)
2x-y=3-m -> 10x-5y=15-5m (2)

(2)-(1): 9y=7-15m -> y=(7-15m)/9 (3)

5x-7y=5m+4 (4)
2x-y=3-m -> 14x-7y=21-7m (5)

(5)-(4): 9x=17-12m -> x= (17-12m)/9 (6)

(3)+(6): x+y=(17-12m)/9+(7-15m)/9=(24-27m)/9=(8-9m)/3

x+y>=4 -> (8-9m)/3>=4 -> 8-9m>=12 -> 9m<=-4 -> m<=-4/9

由2X-Y=3-M得X=(3-M+Y)/2
代入5X-7Y=5M+4得Y=(7-15M)/9
由X+Y不小于4得[3-M+(7-15M)/9]/2+(7-15M)/9不小于4,得M小于等于44/54

先解方程得 x=(17-12m)/9,y=(7-15m)/9
x+y=(24-27m)/9>=4
就锝m<=-4/9