I want to calculate the equipotential lines for $f(x, y) = x + y + |x| + |y|$. The domain is $ℝ^2$ and range $[0, \infty)$. I started like this:
$$ x + y + |x| + |y| = c \ge 0 \\ y + |y| = c - x - |x| $$
But I can't continue any further, I don't know how to get rid of the $|y|$. How can I solve the last equation by $y$?