1. **State the problem:** We are given two points $(|x|,4)$ and $(3,y^2)$ that are equal, and these points lie in the second quadrant. We need to find $x+y$. 2. **Understand the coordinates:** Since the points are equal, their coordinates must be equal: $$|x| = 3 \quad \text{and} \quad 4 = y^2$$ 3. **Solve for $x$:** From $|x|=3$, $x$ can be either $3$ or $-3$. Since the points lie in the second quadrant, where $x$ is negative, we have: $$x = -3$$ 4. **Solve for $y$:** From $4 = y^2$, we get: $$y = \pm 2$$ 5. **Determine the correct $y$ value:** In the second quadrant, $y$ is positive, so: $$y = 2$$ 6. **Calculate $x + y$:** $$x + y = -3 + 2 = -1$$ **Final answer:** $$x + y = -1$$