1. **State the problem:** Simplify the expression $$-\left(3 - 5\left(x - 2y\right)\right) + 2\left(-2x + y\right)$$. 2. **Apply the distributive property:** Distribute the minus sign and the 2 across the parentheses: $$-\left(3 - 5x + 10y\right) + \left(-4x + 2y\right)$$ 3. **Distribute the minus sign inside the first parentheses:** $$-3 + 5x - 10y - 4x + 2y$$ 4. **Combine like terms:** Group the $x$ terms: $5x - 4x = x$ Group the $y$ terms: $-10y + 2y = -8y$ Constant term: $-3$ 5. **Write the simplified expression:** $$x - 8y - 3$$ **Final answer:** $x - 8y - 3$