Determine the value of \( y \) in the system of equations below \( \begin{array}{l}x-2 y=5 \\ 2 x-3 y=10 \\ \text { y }=5 \\ 0 y=0 \\ 0 y=1 \\ y=7\end{array} \)

To determine the value of \( y \) in the given system of equations, we can first analyze the conditions provided: 1. The equation \( y = 5 \) directly gives us one potential value for \( y \). 2. The equation \( 0y = 0 \) is always true for any \( y \) and doesn’t provide a specific value. 3. The equation \( 0y = 1 \) is a contradiction, meaning there is no possible value for \( y \) that satisfies this equation. 4. Finally, \( y = 7 \) gives us another potential value. However, we focus on finding a consistent solution from the first two equations in the actual linear system. We can substitute: From \( x - 2y = 5 \): \[ x = 5 + 2y \] Substituting \( x \) into the second equation: \[ 2(5 + 2y) - 3y = 10 \] \[ 10 + 4y - 3y = 10 \] \[ 10 + y = 10 \] \[ y = 10 - 10 \] \[ y = 0 \] Here, \( y \) takes the value of \( 0 \), which is not one of the given direct values \( (5, 7) \). Nevertheless, it’s a derived value showing that there’s inconsistency in the provided equations for specific values of \( y \). To summarize, the derived value from the first two equations is: \[ \boxed{0} \] However, among the directly mentioned values, \( y = 5 \) stands out as a given valid potential.