Q:

Determine the region bounded by the inequalities

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 $x$:
$$
-x \leq 0 \leq 1 + y \\
$$
Or: 
$$
-y - 1 \leq 0 \leq x \\
$$
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.

A:

The inequalities are:
$$y\le 1-x$$
$$y\ge -x$$
$$y\ge 0$$
$$y\le x$$
You should graph these and determine the region where all the inequalities hold. Here is a picture of what it should look like

