1. **State the problem:** Solve the system of equations using the addition method: $$-3x - 10y = 1$$ $$30x + 100y = -9$$ 2. **Multiply the first equation to align coefficients:** Multiply the first equation by 10 to make the coefficients of $y$ opposites: $$10(-3x - 10y) = 10(1)$$ $$-30x - 100y = 10$$ 3. **Add the two equations:** $$(-30x - 100y) + (30x + 100y) = 10 + (-9)$$ Simplify: $$0 = 1$$ 4. **Interpret the result:** Since $0 \neq 1$, the system is inconsistent and has no solution. **Final answer:** The system has no solution; the lines are parallel.