1. **State the problem:** Solve the system of equations by substitution: $$-6x - 2y = 26$$ $$x = 7y + 3$$ 2. **Substitution method:** Since the second equation gives $x$ in terms of $y$, substitute $x = 7y + 3$ into the first equation. 3. Substitute: $$-6(7y + 3) - 2y = 26$$ 4. Distribute $-6$: $$-42y - 18 - 2y = 26$$ 5. Combine like terms: $$-44y - 18 = 26$$ 6. Add 18 to both sides: $$-44y - 18 + 18 = 26 + 18$$ $$-44y = 44$$ 7. Divide both sides by $-44$: $$y = \frac{44}{\cancel{-44}}\cancel{-1} = -1$$ 8. Substitute $y = -1$ back into $x = 7y + 3$: $$x = 7(-1) + 3 = -7 + 3 = -4$$ 9. **Final answer:** The solution to the system is $$(x, y) = (-4, -1)$$