Kenneth claims that (2,0) is the point of intersection of the lines y= -2x+4 and y=x-2. is he correct? how do you know?

Kenneth is correct because when you put the coordinates in to replace x and y you get 0=-2(2)+4 and simplifying that you get 0=-4+4, and simplifying it one more time gives you 0=0, which is true. The other problem, y=x-2 is true for the same reasons. You put in the coordinates and you get 0=2-2 and 2-2=0, so therefore it also checks.