Solve {l}{y_{3}y_{4}=2(b^2-2x_{0}+4y_{m})}{y_{3}+y_{4}=-2y}

$$\left\{ \begin{array} { l } { y _ { 3 } y _ { 4 } = 2 ( b ^ { 2 } - 2 x _ { 0 } + 4 y _ { m } ) } \\ { y _ { 3 } + y _ { 4 } = - 2 y } \end{array} \right.$$

Solve for y_3, y_4, b, x_0, y_m, y

$$\left\{\begin{matrix}\\y\in \mathrm{C}\text{, }y_{3}=-\frac{2\left(2x_{0}-4y_{m}-b^{2}\right)}{y_{4}}\text{, }y_{4}=\sqrt{4x_{0}+y^{2}-8y_{m}-2b^{2}}-y\text{, }b\in \mathrm{C}\setminus \sqrt{2\left(x_{0}-2y_{m}\right)},-\sqrt{2\left(x_{0}-2y_{m}\right)}\text{, }x_{0}\in \mathrm{C}\text{, }y_{m}\in \mathrm{C}\text{; }y\in \mathrm{C}\text{, }y_{3}=-\frac{2\left(2x_{0}-4y_{m}-b^{2}\right)}{y_{4}}\text{, }y_{4}=-\sqrt{4x_{0}+y^{2}-8y_{m}-2b^{2}}-y\text{, }b\in \mathrm{C}\setminus \sqrt{2\left(x_{0}-2y_{m}\right)},-\sqrt{2\left(x_{0}-2y_{m}\right)}\text{, }x_{0}\in \mathrm{C}\text{, }y_{m}\in \mathrm{C}\text{; }y\in \mathrm{C}\text{, }y_{3}=-2y\text{, }y_{4}=0\text{, }b=\sqrt{2\left(x_{0}-2y_{m}\right)}\text{, }x_{0}\in \mathrm{C}\text{, }y_{m}\in \mathrm{C}\text{; }y\in \mathrm{C}\text{, }y_{3}=-2y\text{, }y_{4}=0\text{, }b=-\sqrt{2\left(x_{0}-2y_{m}\right)}\text{, }x_{0}\in \mathrm{C}\text{, }y_{m}\in \mathrm{C}\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }y_{3}=-\frac{2\left(2x_{0}-4y_{m}-b^{2}\right)}{y_{4}}\text{, }y_{4}=\sqrt{4x_{0}+y^{2}-8y_{m}-2b^{2}}-y\text{, }b\in \mathrm{C}\setminus \sqrt{2\left(x_{0}-2y_{m}\right)}\text{, }arg(y)<\pi \text{ or }y=0,-\sqrt{2\left(x_{0}-2y_{m}\right)}\text{, }arg(y)<\pi \text{ or }y=0\text{, }x_{0}\in \mathrm{C}\text{, }y_{m}\in \mathrm{C}\text{, }&arg(y)\geq \pi \text{ and }y\neq 0\\y\in \mathrm{C}\text{, }y_{3}=-\frac{2\left(2x_{0}-4y_{m}-b^{2}\right)}{y_{4}}\text{, }y_{4}=-\sqrt{4x_{0}+y^{2}-8y_{m}-2b^{2}}-y\text{, }b\in \mathrm{C}\setminus \sqrt{2\left(x_{0}-2y_{m}\right)}\text{, }y=0\text{ or }arg(y)\geq \pi ,-\sqrt{2\left(x_{0}-2y_{m}\right)}\text{, }y=0\text{ or }arg(y)\geq \pi \text{, }x_{0}\in \mathrm{C}\text{, }y_{m}\in \mathrm{C}\text{, }&y\neq 0\text{ and }arg(y)<\pi \end{matrix}\right.$$