Determine the region bounded by the inequalities: $$ 0 \leq x + y \leq 1 \\ 0 \leq x - y \leq x + y $$
I don't know what to solve for first, so I just added them:
$$ 0 \leq x \leq 1 + x + y \\ $$
I guess I can subtract $x$:
$$ -x \leq 0 \leq 1 + y \\ $$
$$ -y - 1 \leq 0 \leq x \\ $$
So from this inequality, it looks like some area in the 4th quadrant because $x \geq 0$ means everything to the right of the $y$-axis, and $-y - 1 \leq 0$ means $- 1 \leq y$ which is above the line $y = -1$. However, it looks like I'm analyzing incorrectly as the answer says that it is some area above $y = 0$. I'm not sure what I'm doing wrong.