1. **State the problem:** Find the point of intersection of the two lines given by the equations: $$-2x + y = -5$$ $$y = \frac{1}{2}x - 2$$ 2. **Use substitution method:** Since the second equation is already solved for $y$, substitute $y = \frac{1}{2}x - 2$ into the first equation. 3. **Substitute and simplify:** $$-2x + \left(\frac{1}{2}x - 2\right) = -5$$ $$-2x + \frac{1}{2}x - 2 = -5$$ 4. **Combine like terms:** $$\left(-2 + \frac{1}{2}\right)x - 2 = -5$$ $$\left(-\frac{4}{2} + \frac{1}{2}\right)x - 2 = -5$$ $$-\frac{3}{2}x - 2 = -5$$ 5. **Isolate $x$:** Add 2 to both sides: $$-\frac{3}{2}x = -5 + 2$$ $$-\frac{3}{2}x = -3$$ 6. **Divide both sides by $-\frac{3}{2}$:** $$x = \frac{-3}{-\frac{3}{2}} = -3 \times \frac{2}{-3} = \cancel{-3} \times \frac{2}{\cancel{-3}} = 2$$ 7. **Find $y$ by substituting $x=2$ into the second equation:** $$y = \frac{1}{2} \times 2 - 2 = 1 - 2 = -1$$ 8. **Final answer:** The lines intersect at the point $$\boxed{(2, -1)}$$.