1. **State the problem:** We need to find the value of $y$ that satisfies the system of equations: $$9x + 5y = 8$$ $$3x - y = 4$$ 2. **Use substitution or elimination method:** Here, we will use substitution. From the second equation, solve for $y$: $$3x - y = 4 \implies y = 3x - 4$$ 3. **Substitute $y$ into the first equation:** $$9x + 5(3x - 4) = 8$$ 4. **Simplify and solve for $x$:** $$9x + 15x - 20 = 8$$ $$24x - 20 = 8$$ $$24x = 8 + 20$$ $$24x = 28$$ 5. **Divide both sides by 24:** $$x = \frac{28}{24} = \frac{\cancel{28}}{\cancel{24}} = \frac{7}{6}$$ 6. **Substitute $x = \frac{7}{6}$ back into $y = 3x - 4$ to find $y$:** $$y = 3 \times \frac{7}{6} - 4 = \frac{21}{6} - 4 = \frac{21}{6} - \frac{24}{6} = \frac{21 - 24}{6} = \frac{-3}{6} = -\frac{1}{2}$$ **Final answer:** The $y$-value of the solution is $-\frac{1}{2}$, which corresponds to option A.