Question 1015623
Assume that y is not equal to 0.

Then {{{10x^2-9xy+2y^2 = (5x - 2y)(2x - y) = 0}}}

==> 5x - 2y = 0 or 2x - y = 0

==> x/y = 2/5 or x/y = 1/2.

Therefore there are two possibilities for x/y, namely 2/5 or 1/2.