Solve a simultaneous equation. How do we solve $|b-y|=b+y-2\;and\;|b+y|=b+2$? I have tried to square them and factorize them but got confused by and and or conditions.

We always have $b+y-|b-y|=2\min(b,y)$ and from the first of the equations given, this is $2$.  Therefore, we know that
$$
\min(b,y)=1
$$
Since we know that $\min(b,y)=1$, we know that $b+y>0$ and so $|b+y|=b+y$. Therefore, the second equation is $b+y=b+2$, which gives us
$$
y=2
$$
So the solution is $b=1$ and $y=2$.
