Question

若方程组﹛3x+y=k+1 x+3y=3 的解为x,y,且2＜k＜4,则x-y的取值范围是

Answer 1

3x+y=k+1 ①

x+3y=3 ②

①-②*3得 y-9y=k+1-9

-8y=k-8

y=1-k/8

x=3-3（1-k/8)=3-3+3k/8=3k/8

x-y=3k/8-(1-k/8)=k/2-1

2