1. **State the problem:** We are given two equations of lines: $$-7x - 6y = 4$$ and $$x = -3y + 8$$ We want to find the values of $x$ and $y$ where these two lines intersect. 2. **Use substitution method:** Since the second equation expresses $x$ in terms of $y$, we can substitute $x = -3y + 8$ into the first equation. 3. **Substitute and simplify:** $$-7(-3y + 8) - 6y = 4$$ Distribute $-7$: $$21y - 56 - 6y = 4$$ Combine like terms: $$15y - 56 = 4$$ 4. **Solve for $y$:** Add 56 to both sides: $$15y - \cancel{56} + 56 = 4 + 56$$ $$15y = 60$$ Divide both sides by 15: $$\frac{15y}{\cancel{15}} = \frac{60}{\cancel{15}}$$ $$y = 4$$ 5. **Find $x$ using $y=4$:** Substitute back into $x = -3y + 8$: $$x = -3(4) + 8$$ $$x = -12 + 8$$ $$x = -4$$ 6. **Final answer:** The lines intersect at the point $$(x, y) = (-4, 4)$$