题目内容
In the rectangular coordinates，abscissa and ordinate of the intersection point of the lines y=x-k and y=kx+2 are integers for imteger k，then the number of the possible values of k is
（英汉小词典：abscissa横坐标；ordinate纵坐标；intersectionpoint交点；integer整数）
- A.4
- B.5
- C.6
- D.7
A
分析：让直线y=x-k，y=kx+2组成方程组，消去y，根据x，k均为整数求得k可能的整数解的个数即可．
解答：
，
x-k=kx+2，
（x+1）k=x-2，
k=1+
，
∵x+1可取±1，±3共4个数，
∴相对应的k的值也要有4个．
故选A．
点评：本题考查了直线的相交问题；组成方程组消去一个未知数是解决本题的突破点；找相应的整数解是解决本题的难点．
分析：让直线y=x-k，y=kx+2组成方程组，消去y，根据x，k均为整数求得k可能的整数解的个数即可．
解答：
，x-k=kx+2，
（x+1）k=x-2，
k=1+
，∵x+1可取±1，±3共4个数，
∴相对应的k的值也要有4个．
故选A．
点评：本题考查了直线的相交问题；组成方程组消去一个未知数是解决本题的突破点；找相应的整数解是解决本题的难点．
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