1. **State the problem:** Solve the system of equations: $$\begin{cases}-6x - y = 23 \\ y = 4x + 7 \end{cases}$$ 2. **Use substitution method:** Since the second equation gives $y$ in terms of $x$, substitute $y = 4x + 7$ into the first equation. 3. **Substitute and simplify:** $$-6x - (4x + 7) = 23$$ $$-6x - 4x - 7 = 23$$ $$-10x - 7 = 23$$ 4. **Isolate $x$:** $$-10x = 23 + 7$$ $$-10x = 30$$ 5. **Divide both sides by $-10$:** $$x = \frac{30}{-10}$$ $$x = \cancel{\frac{30}{-10}}\rightarrow -3$$ 6. **Find $y$ by substituting $x = -3$ into $y = 4x + 7$:** $$y = 4(-3) + 7$$ $$y = -12 + 7$$ $$y = -5$$ 7. **Final answer:** $$\boxed{(x, y) = (-3, -5)}$$