1. **State the problem:** Solve the system of linear equations: $$8y = -x - 20$$ $$2y = -5x + 14$$ 2. **Rewrite each equation in terms of $y$:** From the first equation: $$8y = -x - 20 \implies y = \frac{-x - 20}{8} = -\frac{x}{8} - \frac{20}{8} = -\frac{x}{8} - \frac{5}{2}$$ From the second equation: $$2y = -5x + 14 \implies y = \frac{-5x + 14}{2} = -\frac{5x}{2} + 7$$ 3. **Set the two expressions for $y$ equal to each other to find $x$:** $$-\frac{x}{8} - \frac{5}{2} = -\frac{5x}{2} + 7$$ 4. **Multiply both sides by 8 to clear denominators:** $$-x - 20 = -20x + 56$$ 5. **Bring all terms involving $x$ to one side and constants to the other:** $$-x + 20x = 56 + 20$$ $$19x = 76$$ 6. **Solve for $x$:** $$x = \frac{76}{19} = 4$$ 7. **Substitute $x=4$ back into one of the expressions for $y$ (using the first):** $$y = -\frac{4}{8} - \frac{5}{2} = -\frac{1}{2} - \frac{5}{2} = -3$$ **Final answer:** $$\boxed{(x,y) = (4, -3)}$$