k为那些负数时,方程组3x+2y=k+1,4x+3y=k-1的解适合x>y?

题目

k为那些负数时,方程组3x+2y=k+1,4x+3y=k-1的解适合x>y?

答案

3x+2y=k+1,4x+3y=k-1,通分有,12x+8y=4k+4,12x+9y=3k-3,相减得,y=-k-7,代入得,x=k+5,这样,x>y相当于x-y=(k+5)-(-k-7)=2k+12>0,因此k>-6,k为大于-6的负数时,方程组3x+2y=k+1,4x+3y=k-1的解适合x>y.....