1. Stating the problem: Solve the system of equations $$y = -2x - 1$$ $$3x - 4y = -40$$ 2. Use substitution method since $y$ is already expressed in terms of $x$ in the first equation. 3. Substitute $y = -2x - 1$ into the second equation: $$3x - 4(-2x - 1) = -40$$ 4. Simplify the equation: $$3x + 8x + 4 = -40$$ $$11x + 4 = -40$$ 5. Subtract 4 from both sides: $$11x + \cancel{4} - \cancel{4} = -40 - 4$$ $$11x = -44$$ 6. Divide both sides by 11: $$\frac{11x}{\cancel{11}} = \frac{-44}{\cancel{11}}$$ $$x = -4$$ 7. Substitute $x = -4$ back into the first equation to find $y$: $$y = -2(-4) - 1$$ $$y = 8 - 1$$ $$y = 7$$ 8. Final answer: The solution to the system is $$\boxed{(x, y) = (-4, 7)}$$