What is the \( y \)-coordinate for the solution to the system of equations? \( \left\{\begin{array}{l}6 x-3 y=-7 \\ 2 x+3 y=-9\end{array}\right. \) Enter your answer as the correct value, like this: 42 If your answer is a fraction, enter it in simplest form, formatted like this: \( 3 / 14 \)

To solve the system of equations \( \left\{\begin{array}{l}6 x-3 y=-7 \\ 2 x+3 y=-9\end{array}\right. \), we can use the method of substitution or elimination. First, we can simplify the first equation by dividing everything by 3: \[ 2x - y = -\frac{7}{3} \] So, \( y = 2x + \frac{7}{3} \). Now, we can substitute \( y \) into the second equation: \[ 2x + 3(2x + \frac{7}{3}) = -9 \] This simplifies to: \[ 2x + 6x + 7 = -9 \] So: \[ 8x + 7 = -9 \] Subtracting 7 from both sides gives us: \[ 8x = -16 \] Thus: \[ x = -2 \] Finally, substitute \( x = -2 \) back into our expression for \( y \): \[ y = 2(-2) + \frac{7}{3} = -4 + \frac{7}{3} = -\frac{12}{3} + \frac{7}{3} = -\frac{5}{3} \] Therefore, the \( y \)-coordinate for the solution to the system of equations is \( \frac{-5}{3} \).