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Home » Expand: \( xy - x = 2y + 3 \). - Midis

Expand: \( xy - x = 2y + 3 \). - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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and $ L $ is a multiple of 7 (since pipes are seven units long and tot...
L \equiv 1 \pmod{13} \quad ext{and} \quad L \equiv 0 \pmod{7}
L \equiv 0 \pmod{7} \
Use the Chinese Remainder Theorem. Let $ L = 7k $. Substitute into the...
7k \equiv 1 \pmod{13}
We solve for $ k $: find the modular inverse of 7 modulo 13.
$ 7 \cdot 1 = 7
$ 7 \cdot 2 = 14 \equiv 1 \pmod{13} $
So $ 7^{-1} \equiv 2 \pmod{13} $
k \equiv 2 \pmod{13} \Rightarrow k = 13m + 2

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