Let $x,y \in R$ such that $|x+y| + |x-y| = 2$ 
Let $x,y \in R$ such that $|x+y| + |x-y| = 2$, then find maximum values of $x^2 - 6x + y^2$ and $x^2 + y^2 + 10y$.

How do I go about solving this question? Is it possible to find all real values of $x$ and $y$ from the first equation? Please help.

Guide:
Notice that $|x+y|+|x-y|=2$ describes the boundary of a  square.
$x^2-6x+y^2=(x-3)^2+y^2-9$
The largest value of $y^2$ is $1$. Given that $-1 \le x \le 1$. Try to solve the $-1 \le x \le 1$, how would you optimize $(x-3)^2$.
