12. The real numbers $x$ and $y$ satisfy the equation $(2 x-3 y)^{2}+(3 x-1)^{2}=0$. What is the value of $x+y$?
(A) $1 / 3$
(B) $5 / 9$
(C) 1
(D) $1 / 2$
(E) $3 / 4$
(12) The correct answer is $(B)$.

Since the expression is the sum of two squares, it vanishes if and only if both quantities are zero. It follows that $x=\frac{1}{3}$ and $\frac{2}{3}-3 y=0$, i.e., $y=\frac{2}{9}$. Therefore, $x+y=\frac{1}{3}+\frac{2}{9}=\frac{5}{9}$. Question proposed by Paolo Francini.