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If $a + x = b + y = c + z + 1$, where $a, b, c, x, y, z$ are non-zero distinct real numbers, then $\begin{vmatrix} x & a+y & x+a \ y & b+y & y+b \ z & c+y & z+c \end{vmatrix}$ is equal to:
(1) $y(b - a)$
(2) $y(a - b)$
(3) $0$
(4) $y(a - c)$
BETA
