1. **State the problem:** Find the point of intersection of the two lines given by the equations: $$y = -10x - 3$$ $$y = 2x + 9$$ 2. **Set the equations equal to find the intersection:** Since both expressions equal $y$, set them equal to each other: $$-10x - 3 = 2x + 9$$ 3. **Solve for $x$:** Add $10x$ to both sides: $$\cancel{-10x} + 10x - 3 = 2x + 10x + 9$$ $$-3 = 12x + 9$$ Subtract 9 from both sides: $$-3 - 9 = 12x + \cancel{9} - 9$$ $$-12 = 12x$$ Divide both sides by 12: $$\frac{-12}{\cancel{12}} = \frac{12x}{\cancel{12}}$$ $$-1 = x$$ 4. **Find $y$ by substituting $x = -1$ into one of the original equations:** Using $y = 2x + 9$: $$y = 2(-1) + 9 = -2 + 9 = 7$$ 5. **Final answer:** The lines intersect at the point $$\boxed{(-1, 7)}$$