1. **State the problem:** Solve the system of equations using the elimination method: $$-2x + 2y = -12$$ $$2x + 4y = 12$$ 2. **Elimination method:** We add or subtract the equations to eliminate one variable. 3. Add the two equations: $$(-2x + 2y) + (2x + 4y) = -12 + 12$$ Simplify: $$\cancel{-2x} + 2y + \cancel{2x} + 4y = 0$$ $$6y = 0$$ 4. Solve for $y$: $$y = \frac{0}{6} = 0$$ 5. Substitute $y=0$ into the first equation: $$-2x + 2(0) = -12$$ $$-2x = -12$$ 6. Solve for $x$: $$x = \frac{-12}{-2} = 6$$ 7. **Final answer:** The unique solution is $$(6, 0)$$