1. **State the problem:** Solve the system of linear equations: $$y = 0.5x + 4$$ $$-\frac{1}{3}x + y = -2$$ 2. **Use substitution method:** Since $y$ is already expressed in terms of $x$ in the first equation, substitute $y = 0.5x + 4$ into the second equation. 3. **Substitute and simplify:** $$-\frac{1}{3}x + (0.5x + 4) = -2$$ Combine like terms: $$-\frac{1}{3}x + 0.5x + 4 = -2$$ Convert decimals to fractions for clarity: $0.5 = \frac{1}{2}$ $$-\frac{1}{3}x + \frac{1}{2}x + 4 = -2$$ 4. **Find common denominator and combine $x$ terms:** Common denominator is 6: $$-\frac{2}{6}x + \frac{3}{6}x + 4 = -2$$ $$\left(-\frac{2}{6} + \frac{3}{6}\right)x + 4 = -2$$ $$\frac{1}{6}x + 4 = -2$$ 5. **Isolate $x$:** $$\frac{1}{6}x = -2 - 4$$ $$\frac{1}{6}x = -6$$ Multiply both sides by 6: $$\cancel{6} \times \frac{1}{\cancel{6}} x = -6 \times 6$$ $$x = -36$$ 6. **Find $y$ by substituting $x$ back into the first equation:** $$y = 0.5(-36) + 4$$ $$y = -18 + 4$$ $$y = -14$$ 7. **Final answer:** $$\boxed{(x, y) = (-36, -14)}$$