How many solutions does the system of equations have? \( \begin{array}{l}y=-\frac{7}{2} x+11 \\ 7 x+2 y=20 \\ \text { A. } 1 \text { solution } \\ \text { B. no solution } \\ \text { C. infinitely many solutions } \\ \text { D. cannot be determined }\end{array} \)

To determine how many solutions the system of equations has, we can analyze the equations graphically or algebraically. The first equation, \( y = -\frac{7}{2} x + 11 \), represents a line with a slope of \(-\frac{7}{2}\). The second equation can be rewritten in slope-intercept form. Rearranging \( 7x + 2y = 20 \) gives us \( y = -\frac{7}{2}x + 10 \). Now, notice that both lines have the same slope of \(-\frac{7}{2}\) but different y-intercepts (11 and 10, respectively). This means that the lines are parallel and will never intersect, indicating that there is no solution to the system. Therefore, the answer is **B. no solution**.