1. **State the problem:** Solve the system of inequalities: $$y < 2x - 3$$ $$y > 5$$ 2. **Understand the inequalities:** - The first inequality $y < 2x - 3$ means the solution region is all points below the line $y = 2x - 3$. - The second inequality $y > 5$ means the solution region is all points above the horizontal line $y = 5$. 3. **Analyze the lines:** - The line $y = 2x - 3$ has slope 2 and y-intercept -3. - The line $y = 5$ is horizontal. 4. **Find the intersection of the boundary lines:** Set $2x - 3 = 5$ to find where the lines meet: $$2x - 3 = 5$$ $$2x = 5 + 3$$ $$2x = 8$$ $$x = \frac{8}{2}$$ $$x = 4$$ So, the lines intersect at the point $(4, 5)$. 5. **Determine the solution region:** - The first inequality requires $y$ to be less than $2x - 3$. - The second inequality requires $y$ to be greater than 5. Since $y$ must be simultaneously less than $2x - 3$ and greater than 5, the solution region is where these two conditions overlap. 6. **Check if there is an overlap:** - For $x < 4$, $2x - 3 < 5$, so $y < 2x - 3$ is less than 5. - For $x > 4$, $2x - 3 > 5$, so $y$ can be greater than 5 and less than $2x - 3$. Therefore, the solution region is all points where $x > 4$ and $5 < y < 2x - 3$. **Final answer:** $$\boxed{\{(x,y) \mid x > 4,\ 5 < y < 2x - 3\}}$$