1. **State the problem:** Solve the system of linear equations: $$-7x - 6y = -7$$ $$x + 4y = 23$$ 2. **Choose a method:** We will use the substitution or elimination method. Here, substitution is straightforward. 3. **Isolate $x$ in the second equation:** $$x + 4y = 23 \implies x = 23 - 4y$$ 4. **Substitute $x$ into the first equation:** $$-7(23 - 4y) - 6y = -7$$ 5. **Distribute and simplify:** $$-7 \times 23 + 28y - 6y = -7$$ $$-161 + 22y = -7$$ 6. **Isolate $y$:** $$22y = -7 + 161$$ $$22y = 154$$ 7. **Divide both sides by 22:** $$y = \frac{154}{22}$$ $$y = \frac{\cancel{154}^{7 \times 22}}{\cancel{22}^{1 \times 22}} = 7$$ 8. **Substitute $y=7$ back into $x = 23 - 4y$:** $$x = 23 - 4 \times 7$$ $$x = 23 - 28$$ $$x = -5$$ **Final answer:** $$x = -5, \quad y = 7$$