1. **State the problem:** Solve the system of equations by graphing: $$y = \frac{3}{2}x + 1$$ $$y = -3x - 8$$ Find the point where the two lines intersect. 2. **Recall the formula and rules:** The solution to a system of linear equations is the point where the lines intersect, meaning the $x$ and $y$ values satisfy both equations simultaneously. 3. **Graph each line:** - For $$y = \frac{3}{2}x + 1$$, the slope is $\frac{3}{2}$ and the y-intercept is $1$. - For $$y = -3x - 8$$, the slope is $-3$ and the y-intercept is $-8$. 4. **Find the intersection algebraically to confirm:** Set the right sides equal: $$\frac{3}{2}x + 1 = -3x - 8$$ 5. **Solve for $x$:** $$\frac{3}{2}x + 3x = -8 - 1$$ $$\frac{3}{2}x + \frac{6}{2}x = -9$$ $$\frac{9}{2}x = -9$$ $$x = \frac{-9}{\frac{9}{2}} = -9 \times \frac{2}{9}$$ $$x = -2$$ 6. **Find $y$ by substituting $x = -2$ into one equation:** $$y = \frac{3}{2}(-2) + 1 = -3 + 1 = -2$$ 7. **Solution:** The lines intersect at $$(-2, -2)$$. This matches the given solution. **Final answer:** $$\boxed{(-2, -2)}$$