1. **State the problem:** Solve the system of equations: $$y=5x-3$$ $$3x-8y=24$$ 2. **Use substitution method:** Since $y$ is already expressed in terms of $x$ in the first equation, substitute $y=5x-3$ into the second equation. 3. **Substitute and simplify:** $$3x - 8(5x - 3) = 24$$ $$3x - 40x + 24 = 24$$ $$-37x + 24 = 24$$ 4. **Solve for $x$:** $$-37x = 24 - 24$$ $$-37x = 0$$ $$x = 0$$ 5. **Find $y$ using $x=0$:** $$y = 5(0) - 3 = -3$$ 6. **Final answer:** The solution to the system is $$\boxed{(0, -3)}$$.