1. **State the problem:** Solve the system of equations by substitution: $$\begin{cases} x - 2y = 12 \\ y = 3x + 14 \end{cases}$$ 2. **Formula and rules:** Substitution involves replacing one variable with an expression from the other equation. 3. **Substitute $y$ from the second equation into the first:** $$x - 2(3x + 14) = 12$$ 4. **Simplify:** $$x - 6x - 28 = 12$$ 5. **Combine like terms:** $$\cancel{x} - 6x - 28 = 12 \Rightarrow -5x - 28 = 12$$ 6. **Add 28 to both sides:** $$-5x - 28 + 28 = 12 + 28 \Rightarrow -5x = 40$$ 7. **Divide both sides by -5:** $$\frac{-5x}{\cancel{-5}} = \frac{40}{\cancel{-5}} \Rightarrow x = -8$$ 8. **Substitute $x = -8$ back into $y = 3x + 14$:** $$y = 3(-8) + 14 = -24 + 14 = -10$$ 9. **Final answer:** $$\boxed{(x, y) = (-8, -10)}$$