I need to solve this system of two equations for $x\in[0,0.5]$ and $y\in[0.5,1]$, leaving $b\in[-1,1]$ as a parameter in the solutions.
\begin{cases} 6x^2 b-y(2+(-2+y)b)-2x(-2+(2+y)b)=0\\ -2+y(4-6b)+b-x^2 b+6y^2 b-2x(1+(-1+y)b)=0 \end{cases}
WolframAlpha finds only one real solution for $b=0$, $x=1/3$ and $y=2/3$, but there are others.
What I would like to find, if possible, are two functions $y(b)$ and $x(b)$ that yield the solutions.
See WolframAlpha
Geogebra plot: https://www.geogebra.org/calculator/g3592hwy
The only way I was actually able to solve this system is by setting the parameter $b$ to a given number, reducing the system of equation and then solving for $x$ and $y$. See example: for $b=1$ the system of equations becomes
\begin{cases} 6x^2-2xy-y^2=0\\ 6y^2-2xy-x^2-2y-1=0 \end{cases}
whose solutions are $x\approx0.457849, y\approx0.753505$.