Show that if x is a nonzero rational number, then there is a unique rational number y such that xy = 2

xy = 2

y = 2/x . . . solve for y

Since the equation is solved for y, this is the one and only value for y that makes the equation true. Further, since y is shown as a ration of 2 and x and x is a nonzero rational number, y is a rational number. Thus, y is a unique rational number.

Is this proof correct, or am I missing something?