12. The system of equations $\left\{\begin{array}{l}x+3 y=3, \\ || x|-| y||=1\end{array}\right.$ has $(\quad)$ solutions.
(A) 1
(B) 2
(C) 3
(D) 4
(E) 8
12. C.

Graph the functions $x+3 y=3,|| x|-| y||=1$ (as shown in Figure 3), the two functions have three intersection points: $(-3,2)$, $(0,1),\left(\frac{3}{2}, \frac{1}{2}\right)$