(a) Find all integers $x$ and $y$ such that

$$6 x+2 y \equiv 3 \quad(\bmod 53) \quad \text { and } \quad 17 x+4 y \equiv 7 \quad(\bmod 53)$$

(b) Show that if an integer $n>4$ is composite then $(n-1) ! \equiv 0(\bmod n)$.