Solve the system of equations by any method. \[ \begin{array}{c}-2 y=-1 \\ 7 x-14 y=8\end{array} \] \[ \begin{array}{l}x+2 y\end{array} \]

To solve the system of equations, we start with the first equation: \[ -2y = -1 \] Dividing both sides by -2 gives: \[ y = \frac{1}{2} \] Now, substitute \(y\) into the second equation: \[ 7x - 14y = 8 \] Replacing \(y\) yields: \[ 7x - 14\left(\frac{1}{2}\right) = 8 \] This simplifies to: \[ 7x - 7 = 8 \] Adding 7 to both sides results in: \[ 7x = 15 \] Finally, dividing by 7, we find: \[ x = \frac{15}{7} \] Now that we have \(x\) and \(y\), we can evaluate \(x + 2y\): \[ x + 2y = \frac{15}{7} + 2\left(\frac{1}{2}\right) = \frac{15}{7} + 1 = \frac{15}{7} + \frac{7}{7} = \frac{22}{7} \] So, the final answer is: \[ x + 2y = \frac{22}{7} \]