\(\Leftrightarrow\left\{{}\begin{matrix}3x\left(2x-y\right)-\left(2x-y\right)+3x-1=0\\x^2+y^2=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(3x-1\right)\left(2x-y+1\right)=0\\x^2+y^2=1\end{matrix}\right.\)
TH1: \(\left\{{}\begin{matrix}3x-1=0\\x^2+y^2=1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=\frac{1}{3}\\y^2=\frac{8}{9}\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=\frac{1}{3}\\y=\pm\frac{2\sqrt{2}}{3}\end{matrix}\right.\)
TH2: \(\left\{{}\begin{matrix}2x-y+1=0\\x^2+y^2=1\end{matrix}\right.\)
\(\Rightarrow x^2+\left(2x+1\right)^2=1\)
\(\Leftrightarrow5x^2+4x=0\Rightarrow\left[{}\begin{matrix}x=0\\x=-\frac{4}{5}\end{matrix}\right.\)
