1. **State the problem:** Solve the system of linear equations: $$y = 5x + 37$$ $$2y = -5x - 61$$ 2. **Substitute** the expression for $y$ from the first equation into the second equation: $$2(5x + 37) = -5x - 61$$ 3. **Expand** the left side: $$10x + 74 = -5x - 61$$ 4. **Add** $5x$ to both sides to collect $x$ terms on one side: $$10x + 5x + 74 = -5x + 5x - 61$$ $$15x + 74 = -61$$ 5. **Subtract** 74 from both sides: $$15x + \cancel{74} - \cancel{74} = -61 - 74$$ $$15x = -135$$ 6. **Divide** both sides by 15 to solve for $x$: $$x = \frac{-135}{15}$$ $$x = -9$$ 7. **Substitute** $x = -9$ back into the first equation to find $y$: $$y = 5(-9) + 37$$ $$y = -45 + 37$$ $$y = -8$$ 8. **Solution:** The solution to the system is $$\boxed{(-9, -8)}$$ 9. **Check the options:** The point $(-9, -8)$ matches the third option.