1. **State the problem:** Solve the system of equations: $$y = 3x + 2$$ $$y = 5x$$ 2. **Set the equations equal to each other:** Since both expressions equal $y$, set them equal: $$3x + 2 = 5x$$ 3. **Solve for $x$:** $$3x + 2 = 5x$$ Subtract $3x$ from both sides: $$\cancel{3x} + 2 = \cancel{3x} + 2x \implies 2 = 2x$$ Divide both sides by 2: $$\frac{2}{\cancel{2}} = \frac{2x}{\cancel{2}} \implies 1 = x$$ 4. **Find $y$ by substituting $x=1$ into one of the original equations:** Using $y = 5x$: $$y = 5(1) = 5$$ 5. **Solution:** The solution to the system is: $$(x, y) = (1, 5)$$ 6. **Check if the given point $(2,8)$ satisfies both equations:** For $y = 3x + 2$: $$3(2) + 2 = 6 + 2 = 8$$ For $y = 5x$: $$5(2) = 10$$ Since $8 \neq 10$, $(2,8)$ is not a solution to the system. **Final answer:** The solution to the system is $(1, 5)$, not $(2, 8)$.