1. **State the problem:** Find the point of intersection (POI) of the lines given by the equations $y = -2x + 6$ and $8x - 3y = -4$. 2. **Use substitution or elimination method:** Since $y$ is already expressed in terms of $x$ in the first equation, substitute $y = -2x + 6$ into the second equation. 3. **Substitute:** $$8x - 3(-2x + 6) = -4$$ 4. **Simplify:** $$8x + 6x - 18 = -4$$ 5. **Combine like terms:** $$14x - 18 = -4$$ 6. **Add 18 to both sides:** $$14x - 18 + 18 = -4 + 18$$ $$14x = 14$$ 7. **Divide both sides by 14:** $$\cancel{14}x = \cancel{14}$$ $$x = 1$$ 8. **Find $y$ by substituting $x=1$ into $y = -2x + 6$:** $$y = -2(1) + 6 = -2 + 6 = 4$$ 9. **Final answer:** The point of intersection is at $(1, 4)$.