1. **State the problem:** Solve the system of equations: $$-9x - 4y = 20$$ $$x + 4y = 12$$ 2. **Add the two equations to eliminate $y$:** $$(-9x - 4y) + (x + 4y) = 20 + 12$$ Simplify: $$-9x + x - 4y + 4y = 32$$ $$-8x + \cancel{-4y + 4y} = 32$$ $$-8x = 32$$ 3. **Solve for $x$:** Divide both sides by $-8$: $$x = \frac{32}{-8} = -4$$ 4. **Substitute $x = -4$ into the second equation to find $y$:** $$x + 4y = 12$$ $$-4 + 4y = 12$$ Add 4 to both sides: $$4y = 16$$ Divide both sides by 4: $$y = \frac{16}{4} = 4$$ 5. **Final answer:** $$x = -4, \quad y = 4$$