1. **State the problem:** Solve the system of linear equations: $$5x - y = -5$$ $$3x - 6y = 24$$ 2. **Choose a method:** We will use substitution or elimination. Here, elimination is convenient. 3. **Make coefficients of $y$ equal:** Multiply the first equation by 6 to align the $y$ terms: $$6(5x - y) = 6(-5)$$ $$30x - 6y = -30$$ 4. **Subtract the second equation from this new equation:** $$\cancel{30x} - 6y - (3x - 6y) = -30 - 24$$ $$30x - 6y - 3x + 6y = -54$$ $$27x = -54$$ 5. **Solve for $x$:** $$x = \frac{-54}{27} = -2$$ 6. **Substitute $x = -2$ into the first equation:** $$5(-2) - y = -5$$ $$-10 - y = -5$$ 7. **Solve for $y$:** $$- y = -5 + 10$$ $$- y = 5$$ $$y = -5$$ **Final answer:** $$x = -2, \quad y = -5$$