This is a bonus question, only question I was unable to solve.

An ant wanders over the coordinate plane. Whenever it finds itself stationary at a point with coordinates(xy), it walks without stopping to the point with coordinates (-3x-y,7x+ky), where k is an integer and stops there. What is the value of k if wherever you place the ant on the plane, it returns to that point after a finite number of stops?

Thanks for the help