Given the system of equations, what is the \( y \)-coordinate of the solution? \( \begin{array}{l}5 x-4 y=7 \\ x=5-\frac{3}{2} y \\ 36 / 23 \\ 18 / 23 \\ 36 / 7\end{array} \)

To find the \( y \)-coordinate of the solution for the given system of equations, we can start by substituting the second equation into the first. The second equation is \( x = 5 - \frac{3}{2} y \). Substituting \( x \) in the first equation: \[ 5(5 - \frac{3}{2} y) - 4y = 7 \] This simplifies to: \[ 25 - \frac{15}{2} y - 4y = 7 \] Now, let's convert \( 4y \) into a fraction: \[ 25 - \frac{15}{2} y - \frac{8}{2} y = 7 \] Combining the \( y \)-terms gives us: \[ 25 - \frac{23}{2} y = 7 \] Now, solve for \( y \): \[ \frac{23}{2} y = 25 - 7 \] \[ \frac{23}{2} y = 18 \] Multiplying both sides by \( \frac{2}{23} \): \[ y = \frac{36}{23} \] So, the \( y \)-coordinate of the solution is \( \frac{36}{23} \).