1. **State the problem:** We need to find the graph that represents the system of inequalities: $$y < x + 2$$ $$y > -x + 4$$ 2. **Understand the inequalities:** - The first inequality $y < x + 2$ means the solution region is below the line $y = x + 2$. - The second inequality $y > -x + 4$ means the solution region is above the line $y = -x + 4$. 3. **Find the intersection point of the lines:** Set $x + 2 = -x + 4$ to find where the lines cross. $$x + 2 = -x + 4$$ $$x + x = 4 - 2$$ $$2x = 2$$ $$x = \cancel{\frac{2}{2}}{1}$$ Substitute $x=1$ into $y = x + 2$: $$y = 1 + 2 = 3$$ So, the lines intersect at point $(1, 3)$. 4. **Determine the solution region:** - For $y < x + 2$, the region is below the line. - For $y > -x + 4$, the region is above the other line. The solution is the area below $y = x + 2$ and above $y = -x + 4$. 5. **Check the options:** - Option A shades below both lines (not correct because $y > -x + 4$ requires above that line). - Option B shades above both lines (not correct because $y < x + 2$ requires below that line). - Option C shades to the left of the intersection (not relevant to inequalities in $y$). - Option D shades to the right of the intersection (also not relevant). 6. **Conclusion:** The correct graph is the one where the solution region is between the two lines, below $y = x + 2$ and above $y = -x + 4$, which corresponds to option B. **Final answer:** Option B.