1. **State the problem:** Find the point of intersection of the two lines given by the equations: $$y = -2x + 7$$ $$y = \frac{1}{2}x + 1$$ 2. **Formula and approach:** To find the intersection, set the two expressions for $y$ equal to each other because at the intersection point both lines have the same $x$ and $y$ values. $$-2x + 7 = \frac{1}{2}x + 1$$ 3. **Solve for $x$:** Multiply both sides by 2 to clear the fraction: $$2(-2x + 7) = 2\left(\frac{1}{2}x + 1\right)$$ $$-4x + 14 = x + 2$$ Bring all $x$ terms to one side and constants to the other: $$-4x - x = 2 - 14$$ $$-5x = -12$$ Divide both sides by $-5$: $$x = \frac{-12}{-5} = \frac{12}{5} = 2.4$$ 4. **Find $y$ by substituting $x=2.4$ into one of the original equations:** Using $y = \frac{1}{2}x + 1$: $$y = \frac{1}{2} \times 2.4 + 1 = 1.2 + 1 = 2.2$$ 5. **Conclusion:** The two lines intersect at the point $$\boxed{\left(2.4, 2.2\right)}$$ This means at $x=2.4$, both lines have the same $y$ value of $2.2$, confirming the intersection point.