1. **State the problem:** Solve the system of linear equations: $$x + 3y = -10$$ $$9x + 9y = -18$$ 2. **Use substitution or elimination method:** Here, we use elimination. 3. **Simplify the second equation:** Divide the entire second equation by 9: $$\frac{9x}{9} + \frac{9y}{9} = \frac{-18}{9}$$ $$\cancel{9}x/\cancel{9} + \cancel{9}y/\cancel{9} = -2$$ $$x + y = -2$$ 4. **Rewrite the system:** $$x + 3y = -10$$ $$x + y = -2$$ 5. **Subtract the second equation from the first:** $$(x + 3y) - (x + y) = -10 - (-2)$$ $$x + 3y - x - y = -10 + 2$$ $$2y = -8$$ 6. **Solve for $y$:** $$y = \frac{-8}{2} = -4$$ 7. **Substitute $y = -4$ into $x + y = -2$:** $$x + (-4) = -2$$ $$x - 4 = -2$$ 8. **Solve for $x$:** $$x = -2 + 4 = 2$$ **Final answer:** $$x = 2, \quad y = -4$$