To find the value of \( y \) in the system of equations, we can substitute the expression for \( x \) from the second equation into the first equation. The system of equations is:
\[ 6y + x = -59 \] \[ x = -2y + 9 \]
Now, substitute \( x = -2y + 9 \) into the first equation:
\[ 6y + (-2y + 9) = -59 \]
Simplifying the equation:
\[ 6y - 2y + 9 = -59 \] \[ 4y + 9 = -59 \]
Next, subtract 9 from both sides:
\[ 4y = -59 - 9 \] \[ 4y = -68 \]
Now, divide by 4:
\[ y = \frac{-68}{4} \] \[ y = -17 \]
Thus, the value of \( y \) is \( \boxed{-17} \).