Answer 1

 Substituting \[x = X + 1, y = Y + 1\] in the given equation, we get:
\[\left( X + 1 \right)\left( Y + 1 \right) - \left( X + 1 \right) - \left( Y + 1 \right) + 1 = 0\]
\[ \Rightarrow XY + X + Y + 1 - X - 1 - Y - 1 + 1\]
\[ \Rightarrow XY = 0\]
Hence, the transformed equation is  xy = 0.