Say if I have the following function:
$f_{X,Y}(x,y) \ = \ \left\{ \begin{array}{ll} x^2 + 5x -13, & \mbox{if $2 \leq x \leq 5$ and $0 \leq y \leq x$}, \\ 0, & \mbox{otherwise}. \end{array} \right.$
Can I merge $2\leq x\leq 5~$ and $~0\leq y\leq x~$ into $~2\leq y\leq x\leq 5$?
No, you cannot. For example, $x=2, y=0$ satisfies the first set of inequalities but not the second.