Solve the following system of equations by the substitution method. \( \begin{array}{l}5 x=y+6 \\ 2 x-3 y=4 \\ \text { What is the value of the } y \text {-coordinate? } \\ \text { 14/13 } \\ \text { 13/14 }\end{array} \)

To solve the system of equations using the substitution method, we will first isolate \( y \) in the first equation: 1. From the first equation, \( 5x = y + 6 \) can be rearranged to \( y = 5x - 6 \). Now, substitute \( y \) into the second equation: 2. Replace \( y \) in the second equation \( 2x - 3y = 4 \): \[ 2x - 3(5x - 6) = 4 \] Simplifying this gives: \[ 2x - 15x + 18 = 4 \\ -13x + 18 = 4 \\ -13x = 4 - 18 \\ -13x = -14 \\ x = \frac{14}{13} \] 3. Now, substitute \( x = \frac{14}{13} \) back into the equation for \( y \): \[ y = 5\left(\frac{14}{13}\right) - 6 \\ y = \frac{70}{13} - \frac{78}{13} \\ y = \frac{70 - 78}{13} \\ y = \frac{-8}{13} \] Thus, the \( y \)-coordinate is \( \frac{-8}{13} \). However, since you provided options of \( \frac{14}{13} \) and \( \frac{13}{14} \), it looks like there's a misunderstanding, because the calculated \( y \)-coordinate does not match the choices given. In fact, it seems these choices pertain to a different interpretation or set of computations. Please make sure to check the equations provided or verify the context!