1. **Problem statement:** Find the solution of the system of equations: $$y = 0.5x + 5$$ $$y = 2.5x - 7$$ 2. **Method:** Use the substitution or equalization method by setting the two expressions for $y$ equal to each other. 3. **Set equal:** $$0.5x + 5 = 2.5x - 7$$ 4. **Solve for $x$:** Subtract $0.5x$ from both sides: $$\cancel{0.5x} + 5 = 2.5x - 7 - \cancel{0.5x}$$ $$5 = 2x - 7$$ Add 7 to both sides: $$5 + 7 = 2x - 7 + 7$$ $$12 = 2x$$ Divide both sides by 2: $$\frac{12}{\cancel{2}} = \frac{2x}{\cancel{2}}$$ $$6 = x$$ 5. **Find $y$ by substituting $x=6$ into one of the original equations:** $$y = 0.5 \cdot 6 + 5 = 3 + 5 = 8$$ 6. **Solution:** The solution to the system is $$L = \{(6, 8)\}$$ This means the two lines intersect at the point $(6, 8)$.