1. **State the problem:** Solve the system of linear equations: $$y = -3x - 5$$ $$y = -10x - 9$$ 2. **Set the equations equal to each other** since both equal $y$: $$-3x - 5 = -10x - 9$$ 3. **Solve for $x$:** Add $10x$ to both sides: $$-3x + \cancel{10x} - 5 = \cancel{-10x} - 9 + 10x$$ $$7x - 5 = -9$$ Add $5$ to both sides: $$7x - 5 + 5 = -9 + 5$$ $$7x = -4$$ Divide both sides by $7$: $$x = \frac{-4}{7}$$ 4. **Substitute $x = \frac{-4}{7}$ into one of the original equations to find $y$:** Using $y = -3x - 5$: $$y = -3 \times \frac{-4}{7} - 5 = \frac{12}{7} - 5$$ Convert $5$ to $\frac{35}{7}$: $$y = \frac{12}{7} - \frac{35}{7} = \frac{12 - 35}{7} = \frac{-23}{7}$$ 5. **Final solution:** $$(x, y) = \left(\frac{-4}{7}, \frac{-23}{7}\right)$$