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2 problems match “modular inverse”. Clear

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1. Smallest solution of a linear congruence ●●○○○ 20 ptsWhat is the smallest positive integer $x$ that satisfies the congruence $30x \equiv 42 \pmod{47}$?
2. Solving a four-congruence CRT system ●●●○○ 50 ptsFind the least nonnegative integer $x$ satisfying $x \equiv 4 \pmod{5}$, $x \equiv 2 \pmod{7}$, $x \equiv 2 \pmod{11}$ and $x \equiv 12 \pmod{13}$.