Determine the number of integers $x$ such that $0\le x< 12$ and $x$ satisfies the following system of equations:

\(\begin{align*} &x-1\equiv 1-x\pmod {12}\implies 2x\equiv 2\pmod{12},\\ &x-2\equiv 2-x\pmod{12}\implies 2x\equiv 4\pmod{12}. \end{align*}\)

Since \( 2x\) cannot be equivalent to both two and four in mod 12 we know that there are \(\boxed{0} \) solutions.