1. **State the problem:** Solve the system of equations by substitution and graphing: $$y = 3x - 1$$ $$x = 3y - 1$$ 2. **Use substitution:** From the first equation, we have $y = 3x - 1$. Substitute this into the second equation: $$x = 3(3x - 1) - 1$$ 3. **Simplify the substitution:** $$x = 9x - 3 - 1$$ $$x = 9x - 4$$ 4. **Isolate $x$:** $$x - 9x = -4$$ $$\cancel{1}x - \cancel{9}x = -4$$ $$-8x = -4$$ 5. **Divide both sides by $-8$:** $$x = \frac{-4}{-8}$$ $$x = \frac{1}{2}$$ 6. **Find $y$ using $y = 3x - 1$:** $$y = 3\left(\frac{1}{2}\right) - 1$$ $$y = \frac{3}{2} - 1$$ $$y = \frac{1}{2}$$ 7. **Solution:** The system solution is $$x = \frac{1}{2}, y = \frac{1}{2}$$ 8. **Graph interpretation:** The two lines intersect at the point $(\frac{1}{2}, \frac{1}{2})$, confirming the solution.