1. **State the problem:** Solve the system of equations by substitution: $$\begin{cases} x = 2y - 6 \\ y = 3x - 7 \end{cases}$$ 2. **Use substitution method:** Since the first equation expresses $x$ in terms of $y$, substitute $x = 2y - 6$ into the second equation. 3. Substitute: $$y = 3(2y - 6) - 7$$ 4. Simplify the right side: $$y = 6y - 18 - 7$$ $$y = 6y - 25$$ 5. Rearrange to isolate $y$: $$y - 6y = -25$$ $$\cancel{y} - 6\cancel{y} = -25$$ $$-5y = -25$$ 6. Divide both sides by $-5$: $$\frac{-5y}{\cancel{-5}} = \frac{-25}{\cancel{-5}}$$ $$y = 5$$ 7. Substitute $y=5$ back into the first equation to find $x$: $$x = 2(5) - 6$$ $$x = 10 - 6$$ $$x = 4$$ **Final answer:** $$\boxed{(x, y) = (4, 5)}$$