1. **State the problem:** Solve the system of linear equations: $$-2x - y = -9$$ $$5x - 2y = 18$$ 2. **Formula and method:** We will use the substitution or elimination method. Here, elimination is convenient. 3. **Eliminate one variable:** Multiply the first equation by 2 to align coefficients of $y$: $$2(-2x - y) = 2(-9) \Rightarrow -4x - 2y = -18$$ 4. **Write the system now:** $$-4x - 2y = -18$$ $$5x - 2y = 18$$ 5. **Subtract the first from the second:** $$\cancel{-4x} - 2y - (\cancel{-4x} - 2y) = 18 - (-18)$$ $$5x - 2y - (-4x - 2y) = 18 + 18$$ $$5x - 2y + 4x + 2y = 36$$ $$9x = 36$$ 6. **Solve for $x$:** $$x = \frac{36}{9} = 4$$ 7. **Substitute $x=4$ into the first original equation:** $$-2(4) - y = -9$$ $$-8 - y = -9$$ 8. **Solve for $y$:** $$- y = -9 + 8$$ $$- y = -1$$ $$y = 1$$ 9. **Final answer:** $$\boxed{(x, y) = (4, 1)}$$