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

Solve the system of equations \( 5x-4y=7,x=5-\frac{3}{2}y \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}5x-4y=7\\x=5-\frac{3}{2}y\end{array}\right.\) - step1: Substitute the value of \(x:\) \(5\left(5-\frac{3}{2}y\right)-4y=7\) - step2: Simplify: \(25-\frac{23}{2}y=7\) - step3: Move the constant to the right side: \(-\frac{23}{2}y=7-25\) - step4: Subtract the numbers: \(-\frac{23}{2}y=-18\) - step5: Change the signs: \(\frac{23}{2}y=18\) - step6: Multiply by the reciprocal: \(\frac{23}{2}y\times \frac{2}{23}=18\times \frac{2}{23}\) - step7: Multiply: \(y=\frac{36}{23}\) - step8: Substitute the value of \(y:\) \(x=5-\frac{3}{2}\times \frac{36}{23}\) - step9: Calculate: \(x=\frac{61}{23}\) - step10: Calculate: \(\left\{ \begin{array}{l}x=\frac{61}{23}\\y=\frac{36}{23}\end{array}\right.\) - step11: Check the solution: \(\left\{ \begin{array}{l}x=\frac{61}{23}\\y=\frac{36}{23}\end{array}\right.\) - step12: Rewrite: \(\left(x,y\right) = \left(\frac{61}{23},\frac{36}{23}\right)\) The solution to the system of equations is \( (x, y) = \left(\frac{61}{23}, \frac{36}{23}\right) \). Therefore, the \( y \)-coordinate of the solution is \( \frac{36}{23} \).