Choice A is the correct answer. "First quadrant" implies $x > 0$ and $y > 0$.

1. First Quadrant: $x > 0$ and $y > 0$
2. Bounded by: $x < 4$ (left of vertical line 4) and $y < 3$ (below horizontal line 3)
3. Combine: All four conditions must be met.

?�� Strategic Tip: Always check for quadrant constraints ($x>0, y>0$) in geometry problems.

Choice B is incorrect because it shades the wrong directions (right and up). Choice C is incorrect because it includes regions in other quadrants (negative x and y). Choice D is incorrect because it uses inclusive inequalities (solid lines) when strict ($<$) were specified, and misses quadrant constraints.