$5 x \equiv 1 \pmod 3 \implies x \equiv 2 \pmod 3$ $7 x \equiv 1 \pmod 5 \implies x \equiv 3 \pmod 5$ $9 x \equiv 1 \pmod 7 \implies x \equiv 4 \pmod 7$ $x \equiv 2 \pmod 3 \text{ and }x \equiv 3 \pmod 5 \implies x \equiv a \pmod{15}$ Since $x \equiv 2 \pmod 3$, we have $a \in \{2,5,8,11,14\}$. Since $x$ is also $3 \pmod 5$, we get that $x \equiv 8 \pmod {15}$
$x \equiv 8 \pmod {15} \text{ and }x \equiv 4 \pmod 7 \implies x \equiv b \pmod{105}$ Since $x \equiv 8 \pmod 15$, we have $b \in \{8,23,38,53,68,83,98\}$. Since $x$ is also $4 \pmod 7$, we get that $x \equiv 53 \pmod {105}$