1. **State the problem:** Solve the system of equations using the substitution method: $$-12x - 2y = -6$$ $$6x + y = 3$$ 2. **Isolate one variable in one equation:** From the second equation, solve for $y$: $$6x + y = 3 \implies y = 3 - 6x$$ 3. **Substitute into the first equation:** Replace $y$ in the first equation with $3 - 6x$: $$-12x - 2(3 - 6x) = -6$$ 4. **Simplify and solve for $x$:** $$-12x - 6 + 12x = -6$$ $$(-12x + 12x) - 6 = -6$$ $$0 - 6 = -6$$ $$-6 = -6$$ This is a true statement, meaning the two equations are dependent and represent the same line. 5. **Interpretation:** Since the substitution leads to a true statement without determining a unique $x$, the system has infinitely many solutions. 6. **Express the solution:** Using $y = 3 - 6x$, the solution set is all points $(x, y)$ such that: $$y = 3 - 6x$$ **Final answer:** The system has infinitely many solutions along the line $y = 3 - 6x$.