I've started to study number theory, I completely do not understand from my notes how to work this out. Could anyone show me with simple example how to solve this?
\begin{cases} 3x \equiv 4 \pmod{7}\\ 5x \equiv 9 \pmod{11} \end{cases}
2026-04-01 03:10:45.1775013045
Congruence system \begin{cases} 3x \equiv 4 \pmod{7}\\ 5x \equiv 9 \pmod{11} \end{cases}
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$$3x\equiv 4 \mod 7$$
$$5\times 3x\equiv 4 \times 5 \mod 7$$
$$x\equiv 6 \mod 7$$
$x=7t+6, t\in Z$
$$5x\equiv 9 \mod 11$$
$$35t+30\equiv 9 \mod 11$$
$$2t\equiv 1 \mod 11$$
$$t\equiv 6 \mod 11$$
$t=11k+6, k\in Z$
$$x=77k+48, k\in Z $$