1. **State the problem:** Solve the system of equations by substitution: $$\begin{cases} y = 2x - 10 \\ 2y = x - 8 \end{cases}$$ 2. **Formula and rules:** Substitution involves replacing one variable with an expression from the other equation. 3. **Step 1:** From the first equation, we already have $y$ expressed in terms of $x$: $$y = 2x - 10$$ 4. **Step 2:** Substitute $y = 2x - 10$ into the second equation: $$2y = x - 8$$ becomes $$2(2x - 10) = x - 8$$ 5. **Step 3:** Simplify the left side: $$4x - 20 = x - 8$$ 6. **Step 4:** Move all terms involving $x$ to one side and constants to the other: $$4x - x = -8 + 20$$ which simplifies to $$3x = 12$$ 7. **Step 5:** Solve for $x$: $$x = \frac{12}{3}$$ Show cancellation: $$x = \frac{\cancel{12}}{\cancel{3}} = 4$$ 8. **Step 6:** Substitute $x=4$ back into the first equation to find $y$: $$y = 2(4) - 10 = 8 - 10 = -2$$ 9. **Final answer:** The solution to the system is $$\boxed{(x,y) = (4, -2)}$$