1. **State the problem:** Solve the system of inequalities by graphing: $$y < -2$$ $$y > 10x - 9$$ 2. **Understand the inequalities:** - The first inequality, $$y < -2$$, represents all points below the horizontal line $$y = -2$$. - The second inequality, $$y > 10x - 9$$, represents all points above the line $$y = 10x - 9$$. 3. **Graph the boundary lines:** - For $$y = -2$$, this is a horizontal line crossing the y-axis at -2. - For $$y = 10x - 9$$, this is a line with slope 10 and y-intercept -9. 4. **Determine line types:** - Both inequalities are strict ("<" and ">"), so both boundary lines are dotted (not solid). 5. **Shade the solution region:** - Shade below the line $$y = -2$$. - Shade above the line $$y = 10x - 9$$. 6. **Find the intersection region:** - The solution is the region where these shaded areas overlap. 7. **Check intersection points:** - Find where $$y = -2$$ intersects $$y = 10x - 9$$: $$-2 = 10x - 9$$ $$-2 + 9 = 10x$$ $$7 = 10x$$ $$x = \frac{7}{10}$$ - So the lines intersect at $$\left(\frac{7}{10}, -2\right)$$. 8. **Summary:** - The solution is all points $$\left(x,y\right)$$ such that $$y < -2$$ and $$y > 10x - 9$$. - Graphically, this is the region below the dotted horizontal line $$y = -2$$ and above the dotted line $$y = 10x - 9$$, between and beyond their intersection at $$\left(\frac{7}{10}, -2\right)$$. **Final answer:** The solution region is the area below $$y = -2$$ and above $$y = 10x - 9$$ with both boundary lines dotted.