x.y = x:y

=> x.y.y = x

=> xy² = x

=> y² = 1

=> y = \(\pm1\)

* x + y = xy

\(\Rightarrow\dfrac{x+y}{xy}=\dfrac{x}{xy}+\dfrac{y}{xy}=\dfrac{1}{y}+\dfrac{1}{x}=1\)

If y = 1

=> 1/x = 1 - 1 = 0 --> nonsense

If y = -1

=> 1/x = 1 - [-1] = 2

=> 1/x = 2

=> x = 1/2

So \(\left(x,y\right)=\left(\dfrac{1}{2};-1\right)\)