1. **State the problem:** We are given two linear equations: $$y = \frac{1}{3}x + 2$$ and $$y = 2x - 8$$ We need to find the point where these two lines intersect. 2. **Set the equations equal to find the intersection:** Since both expressions equal $y$, set them equal to each other: $$\frac{1}{3}x + 2 = 2x - 8$$ 3. **Solve for $x$:** Subtract $\frac{1}{3}x$ from both sides: $$\cancel{\frac{1}{3}x} + 2 - \cancel{\frac{1}{3}x} = 2x - \frac{1}{3}x - 8$$ which simplifies to: $$2 = \left(2 - \frac{1}{3}\right)x - 8$$ Calculate the coefficient: $$2 - \frac{1}{3} = \frac{6}{3} - \frac{1}{3} = \frac{5}{3}$$ So: $$2 = \frac{5}{3}x - 8$$ 4. **Add 8 to both sides:** $$2 + 8 = \frac{5}{3}x - 8 + 8$$ $$10 = \frac{5}{3}x$$ 5. **Solve for $x$ by dividing both sides by $\frac{5}{3}$:** $$x = \frac{10}{\frac{5}{3}} = 10 \times \frac{3}{5} = 6$$ 6. **Find $y$ by substituting $x=6$ into one of the original equations:** Using $$y = \frac{1}{3}x + 2$$: $$y = \frac{1}{3} \times 6 + 2 = 2 + 2 = 4$$ 7. **Conclusion:** The lines intersect at the point $$(6, 4)$$. 8. **Check the solution:** Substitute $x=6$ into the second equation: $$y = 2 \times 6 - 8 = 12 - 8 = 4$$ Matches the $y$ value found, confirming the solution. **Final answer:** The lines intersect at $$(6, 4)$$.