simple congruence system problem. This is excercise 1 in George E. Andrews number theory. page 51. How am i supposed to solve this? Thanks very much in advance. I used the cancellation law to get isolate the x. But I don’t know what to do next.
$5x\equiv 4 \pmod 3$
$7x\equiv 6 \pmod 5$
$9x\equiv 8 \pmod 7$

The numbers are very special! Our system is equivalent to $2x\equiv 1$ modulo $3$, $5$, $7$, or equivalently $2x\equiv 1\pmod{105}$.
To solve  $2x\equiv 1\pmod{105}$, rewrite as $2x\equiv 106\pmod{105}$.  This has solution $x\equiv 53\pmod{105}$.
