Confusion with equations lol

[Wow Jr.]

It says that because x is a factor of 2x and xy, it must also be a factor of 2y. Why is it a factor of 2y?

[MS8609]

@Wow-Jr
First of all:

$$2x + 2y = xy $$

All three values (2x, 2y, xy) have a factor. A factor for the values can be x (hint mentions x so we'll stick with x, y is also fine though).
Therefore:

$$2 + {2y\over x} = y $$ $${2y\over x} = y - 2 $$

Because x and y are integers,

$${2y\over x} $$

is an integer (y as an integer minus 2 as an integer leaves an integer result of 2y/x).
Therefore x is a factor of 2y, where:

$$x*{2y\over x}=2y $$

Hope that helps.