\[ \begin{array}{l}\begin{array}{l}\text { Solve the system by the method of your choice. } \\ -2 x+16 y=-14\end{array} \\ \text { Select the correct choice below and fill in any answer boxes present in your choice. The solution set is }\}\} \text {. (Simplify your answer. Type an ordered pair.) } \\ \text { B. There are infinitely many solutions. } \\ \text { C. There is no solution. }\end{array} \]

To solve the equation \(-2x + 16y = -14\), let's first rearrange it into slope-intercept form \(y = mx + b\). Start by isolating \(y\): \[ 16y = 2x - 14 \] \[ y = \frac{1}{8}x - \frac{7}{8} \] Now, this equation represents a line with a slope of \(\frac{1}{8}\) and a y-intercept of \(-\frac{7}{8}\). To determine if this system has a unique solution, infinitely many solutions, or no solution, we need more equations. If we had another linear equation and it turned out to be parallel (same slope) but different y-intercepts, we'd conclude "no solution." Conversely, if it overlaps, we'd say "infinitely many solutions." Since we have only one equation, the best we can conclude is that it defines a line on the plane, thus there's a whole set of solutions along that line. Given that we only have one equation without another to compare with, we conclude: **Solution Set**: There are infinitely many solutions represented by all the points on the line defined by that equation. If you needed to look for a unique point, you’d require additional information or constraints on the variables!