1. **State the problem:** Solve the system of equations by substitution: $$y = 6x$$ $$7x - 8y = -41$$ 2. **Explain substitution method:** We substitute the expression for $y$ from the first equation into the second equation to solve for $x$. 3. **Substitute $y = 6x$ into the second equation:** $$7x - 8(6x) = -41$$ 4. **Simplify the equation:** $$7x - 48x = -41$$ $$-41x = -41$$ 5. **Solve for $x$:** $$x = \frac{-41}{-41} = 1$$ 6. **Find $y$ using $y = 6x$:** $$y = 6(1) = 6$$ 7. **Final answer:** The solution to the system is $$(x, y) = (1, 6)$$