1. **State the problem:** Solve the system of linear equations: $$-9x - 4y = 20$$ $$x + 4y = 12$$ 2. **Choose a method:** We can add the two equations to eliminate $y$ because the coefficients of $y$ are $-4$ and $4$, which sum to zero. 3. **Add the equations:** $$(-9x - 4y) + (x + 4y) = 20 + 12$$ Simplify: $$-9x + x - 4y + 4y = 32$$ $$-8x + \cancel{-4y + 4y} = 32$$ $$-8x = 32$$ 4. **Solve for $x$:** Divide both sides by $-8$: $$x = \frac{32}{-8} = -4$$ 5. **Substitute $x = -4$ into one of the original equations to find $y$:** Using the second equation: $$x + 4y = 12$$ Substitute $x = -4$: $$-4 + 4y = 12$$ Add 4 to both sides: $$4y = 12 + 4 = 16$$ Divide both sides by 4: $$y = \frac{16}{4} = 4$$ 6. **Final answer:** $$x = -4, \quad y = 4$$