Solve the following system of inequalities graphically: $x > 0, y > 0, x \leq 3, y \leq 2$.

The given system of inequalities is:
$1. x > 0$ (Region to the right of the $y$-axis)
$2. y > 0$ (Region above the $x$-axis)
$3. x \leq 3$ (Region to the left of the line $x = 3$)
$4. y \leq 2$ (Region below the line $y = 2$)
To solve this graphically,we plot the lines $x = 0$ (the $y$-axis),$y = 0$ (the $x$-axis),$x = 3$,and $y = 2$.
The solution is the rectangular region in the first quadrant bounded by the vertices $(0, 0), (3, 0), (3, 2),$ and $(0, 2)$.