Just a simple question #5

$\dfrac{x - y}{x} = \dfrac{y}{x}$

$x^2 - xy = xy$

$x^2 = 2xy$

$x = 2y$

So, in the interval of $0 \leq x,y <10$ , the solution of $(x,y)$ that satisfy the equation are : $(2,1);(4,2);(6,3);(8,4)$ . So there are $\boxed{4}$ pairs of solution.

The equation only works when x=2y. x cannot equal 0 because it is in the denominator and cannot equal 5 because y must be less than 10. This only allows x to equal 1 through 4 leaving 4 possibilities.