Question Number 140779 by 676597498 last updated on 12/May/21
$$\begin{cases}{\mathrm{7}{x}\equiv\mathrm{3}\left({mod}\mathrm{5}\right)}\\{\mathrm{5}{x}\equiv\mathrm{3}\left({mod}\mathrm{9}\right)}\end{cases} \\ $$$${solve}\:{for}\:{x} \\ $$
Commented by 676597498 last updated on 12/May/21
$${pls} \\ $$
Answered by mr W last updated on 13/May/21
$$\mathrm{7}{x}=\mathrm{5}{p}+\mathrm{3}\:\Rightarrow{x}=\mathrm{5}{m}+\mathrm{4} \\ $$$$\mathrm{5}{x}=\mathrm{9}{q}+\mathrm{3}\:\Rightarrow{x}=\mathrm{9}{n}+\mathrm{6} \\ $$$$\mathrm{5}{m}+\mathrm{4}=\mathrm{9}{n}+\mathrm{6}\:\Rightarrow{m}=\mathrm{9}{k}+\mathrm{4} \\ $$$$\Rightarrow{x}=\mathrm{5}\left(\mathrm{9}{k}+\mathrm{4}\right)+\mathrm{4}=\mathrm{45}{k}+\mathrm{24} \\ $$$${or}\:{x}\equiv\mathrm{24}\:\left({mod}\:\mathrm{45}\right) \\ $$