1. The problem is to find the point of intersection $(x,y)$ of the two lines given by the equations: $$y = -3x - 5$$ and $$y = -10x - 9$$ 2. To find the intersection, set the right-hand sides equal since at the intersection point both $y$ values are the same: $$-3x - 5 = -10x - 9$$ 3. Solve for $x$ by adding $10x$ to both sides: $$-3x + \cancel{10x} - 5 = \cancel{-10x} - 9 + 10x$$ $$7x - 5 = -9$$ 4. Add 5 to both sides: $$7x - \cancel{5} + \cancel{5} = -9 + 5$$ $$7x = -4$$ 5. Divide both sides by 7: $$x = \frac{-4}{7}$$ 6. Substitute $x = \frac{-4}{7}$ back into one of the original equations to find $y$. Using $y = -3x - 5$: $$y = -3 \times \frac{-4}{7} - 5 = \frac{12}{7} - 5 = \frac{12}{7} - \frac{35}{7} = \frac{-23}{7}$$ 7. Therefore, the point of intersection is: $$(x,y) = \left(\frac{-4}{7}, \frac{-23}{7}\right)$$