1. **State the problem:** We need to find which pair $(x,y)$ satisfies the system of inequalities: $$x - 2y < 5$$ $$y \leq 2x + 5$$ 2. **Check each option:** We substitute each pair into both inequalities to verify. 3. **Option 1: $x = -3$, $y = 6$** - Check $x - 2y < 5$: $$-3 - 2(6) = -3 - 12 = -15 < 5 \quad \text{True}$$ - Check $y \leq 2x + 5$: $$6 \leq 2(-3) + 5 = -6 + 5 = -1 \quad \text{False}$$ 4. **Option 2: $x = -8$, $y = -10$** - Check $x - 2y < 5$: $$-8 - 2(-10) = -8 + 20 = 12 < 5 \quad \text{False}$$ 5. **Option 3: $x = 2$, $y = -2$** - Check $x - 2y < 5$: $$2 - 2(-2) = 2 + 4 = 6 < 5 \quad \text{False}$$ 6. **Option 4: $x = -1$, $y = 3$** - Check $x - 2y < 5$: $$-1 - 2(3) = -1 - 6 = -7 < 5 \quad \text{True}$$ - Check $y \leq 2x + 5$: $$3 \leq 2(-1) + 5 = -2 + 5 = 3 \quad \text{True}$$ 7. **Conclusion:** Only the pair $x = -1$, $y = 3$ satisfies both inequalities. **Final answer:** $x = -1$ and $y = 3$