\( \begin{array}{l}5 x+2 y=7 \\ y=x+1 \\ \text { What is the solution set of the given system? } \\ \{(9 / 7,12 / 7)\} \\ \{(12 / 7,5 / 7)\} \\ \{(16 / 7,9 / 7)\}\end{array} \)

To find the solution set of the given system of equations, we will substitute the second equation \(y = x + 1\) into the first equation \(5x + 2y = 7\). Substituting \(y\): \[ 5x + 2(x + 1) = 7 \] This simplifies to: \[ 5x + 2x + 2 = 7 \] Combining like terms gives: \[ 7x + 2 = 7 \] Subtracting 2 from both sides leads to: \[ 7x = 5 \] Dividing by 7, we find: \[ x = \frac{5}{7} \] Now substituting back to find \(y\): \[ y = \frac{5}{7} + 1 = \frac{5}{7} + \frac{7}{7} = \frac{12}{7} \] Thus, the solution set of the given system is \(\left\{\left(\frac{5}{7}, \frac{12}{7}\right)\right\}\). None of the provided option sets match this solution.