1. **State the problem:** Solve the system of equations: $$9x + 11y = -9$$ $$3x + 4y = -3$$ 2. **Use the substitution or elimination method.** Here, we use elimination for clarity. 3. Multiply the second equation by 3 to align coefficients of $x$: $$3(3x + 4y) = 3(-3) \Rightarrow 9x + 12y = -9$$ 4. Now subtract the first equation from this new equation: $$\cancel{9x} + 12y - (\cancel{9x} + 11y) = -9 - (-9)$$ $$12y - 11y = 0$$ $$y = 0$$ 5. Substitute $y=0$ into the second original equation: $$3x + 4(0) = -3$$ $$3x = -3$$ $$x = \frac{-3}{3} = -1$$ 6. **Final solution:** $$(x, y) = (-1, 0)$$ Note: The provided solution $(\frac{1}{3}, -1)$ does not satisfy both equations. --- **Summary:** The system solution is $$(x, y) = (-1, 0)$$.