1. **State the problem:** Solve the system of equations: $$5x + 4y = -14$$ $$-x - 12y = 14$$ 2. **Choose a method:** We will use substitution or elimination. Here, elimination is convenient. 3. **Eliminate variable $x$:** Multiply the second equation by 5 to align coefficients of $x$: $$5(-x - 12y) = 5(14)$$ $$-5x - 60y = 70$$ 4. **Add the first equation and the new equation:** $$5x + 4y = -14$$ $$-5x - 60y = 70$$ \text{Add: } (5x - 5x) + (4y - 60y) = -14 + 70$$ $$0x - 56y = 56$$ 5. **Simplify:** $$-56y = 56$$ $$y = \frac{56}{-56} = -1$$ 6. **Substitute $y = -1$ into the first equation:** $$5x + 4(-1) = -14$$ $$5x - 4 = -14$$ $$5x = -14 + 4 = -10$$ 7. **Solve for $x$:** $$x = \frac{-10}{5} = -2$$ **Final answer:** $$\boxed{(x, y) = (-2, -1)}$$