Here you can solve it by drawing pictures. In M-set, its image passes through the first, second and fourth quadrants, and the intersection of 2x+3y=4320 with the X axis is (2160,0), and the intersection of the Y axis is (0, 1440). If you want x, y∈N, you can only take it in the first quadrant, obviously in the first place. Y)|4x-3y= 1, x, y∈N}, whose image passes through the first, third and fourth quadrants. 4x-3y= 1 The intersection with the X axis is (1/4,0), and the intersection with the Y axis is (0). Y)|4x-3y= 1, x, y∈N} This set is infinite, and M={(x, y)|2x+3y=4320, x, y∈N} This set is finite.