$$bg+by=+b$$
$\left\{\begin{matrix}\\b=0\text{, }&\text{unconditionally}\\b\in \mathrm{C}\text{, }&g=1-y\end{matrix}\right.$
$\left\{\begin{matrix}\\g=1-y\text{, }&\text{unconditionally}\\g\in \mathrm{C}\text{, }&b=0\end{matrix}\right.$
$\left\{\begin{matrix}\\b=0\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&g=1-y\end{matrix}\right.$
$\left\{\begin{matrix}\\g=1-y\text{, }&\text{unconditionally}\\g\in \mathrm{R}\text{, }&b=0\end{matrix}\right.$