1. **State the problem:** Solve the system of equations: $$2x + 38y = 252$$ and $$\frac{y}{x} = 0.5$$ 2. **Use the ratio to express one variable in terms of the other:** From $$\frac{y}{x} = 0.5$$, we get $$y = 0.5x$$ 3. **Substitute into the first equation:** $$2x + 38(0.5x) = 252$$ 4. **Simplify the equation:** $$2x + 19x = 252$$ $$21x = 252$$ 5. **Solve for $$x$$:** $$x = \frac{252}{21}$$ Show cancellation: $$x = \frac{\cancel{252}}{\cancel{21}} = 12$$ 6. **Find $$y$$ using $$y = 0.5x$$:** $$y = 0.5 \times 12 = 6$$ **Final answer:** $$x = 12, \quad y = 6$$