Solve {l}{bx(2x-y)+(y-1)(2x-y)=bx+y-1}{4x^2+y^2+axy=1}

$$\left. \begin{array} { l } { b x ( 2 x - y ) + ( y - 1 ) ( 2 x - y ) = b x + y - 1 } \\ { 4 x ^ { 2 } + y ^ { 2 } + a x y = 1 } \end{array} \right.$$

Solve for x, y (complex solution)

$$\left\{\begin{matrix}\\x=\frac{1}{2}=0.5\text{, }y=0\text{; }x=0\text{, }y=-1\text{, }&\text{unconditionally}\\x=\frac{y+1}{2}\text{, }y\in \mathrm{C}\text{, }&a=-4\\x=-\frac{-\sqrt{\left(\frac{2b-a}{b}\right)^{2}}b+a-2b}{2\left(4+b^{2}-ab\right)}\text{, }y=\frac{-ab-\sqrt{\left(\frac{2b-a}{b}\right)^{2}}b^{2}+8}{2\left(4+b^{2}-ab\right)}\text{; }x=-\frac{\sqrt{\left(\frac{2b-a}{b}\right)^{2}}b+a-2b}{2\left(4+b^{2}-ab\right)}\text{, }y=\frac{-ab+\sqrt{\left(\frac{2b-a}{b}\right)^{2}}b^{2}+8}{2\left(4+b^{2}-ab\right)}\text{, }&b\neq \frac{\sqrt{a^{2}-16}+a}{2}\text{ and }b\neq \frac{-\sqrt{a^{2}-16}+a}{2}\text{ and }b\neq 0\\x=-\frac{4+b^{2}-ab}{b\left(ab-8\right)}\text{, }y=\frac{b^{2}-4}{ab-8}\text{, }&a=b+\frac{4}{b}\text{ and }b\neq -2\text{ and }b\neq 2\text{ and }b\neq 0\\x=-\frac{y-1}{b}\text{, }y\in \mathrm{C}\text{, }&\left(b=2\text{ and }a=4\right)\text{ or }\left(b=-2\text{ and }a=-4\right)\\x=0\text{, }y=1\text{; }x=-\frac{a}{4}\text{, }y=1\text{, }&b=0\end{matrix}\right.$$

Solve for x, y

$$\left\{\begin{matrix}\\x=\frac{1}{2}=0.5\text{, }y=0\text{, }&\text{unconditionally}\\x=0\text{, }y=-1\text{, }&a\neq -4\\x=\frac{y+1}{2}\text{, }y\in \mathrm{R}\text{, }&a=-4\\x=-\frac{a|b|-2b|\frac{2b-a}{2}|-2b|b|}{2|b|\left(4+b^{2}-ab\right)}\text{, }y=\frac{-ab|b|-2|\frac{2b-a}{2}|b^{2}+8|b|}{2|b|\left(4+b^{2}-ab\right)}\text{; }x=-\frac{a|b|+2b|\frac{2b-a}{2}|-2b|b|}{2|b|\left(4+b^{2}-ab\right)}\text{, }y=\frac{-ab|b|+2|\frac{2b-a}{2}|b^{2}+8|b|}{2|b|\left(4+b^{2}-ab\right)}\text{, }&b\neq 0\text{ and }\left(|a|<4\text{ or }b\neq \frac{-\sqrt{a^{2}-16}+a}{2}\right)\text{ and }\left(|a|<4\text{ or }b\neq \frac{\sqrt{a^{2}-16}+a}{2}\right)\\x=-\frac{4+b^{2}-ab}{b\left(ab-8\right)}\text{, }y=\frac{b^{2}-4}{ab-8}\text{, }&a=b+\frac{4}{b}\text{ and }b\neq 0\text{ and }|b|\neq 2\\x=-\frac{y-1}{b}\text{, }y\in \mathrm{R}\text{, }&\left(b=-2\text{ and }a=-4\right)\text{ or }\left(b=2\text{ and }a=4\right)\\x=0\text{, }y=1\text{; }x=-\frac{a}{4}\text{, }y=1\text{, }&b=0\end{matrix}\right.$$