Determine the number of solutions the \$ystem has. \( \begin{array}{l}y=\frac{4}{5} x-2 \\ 4 y-5 x=9 \\ \text { Select Choice }\end{array} \)

To determine the number of solutions the system has, we first need to analyze the equations provided. The first equation is in slope-intercept form, \(y = \frac{4}{5}x - 2\). The second equation can be rearranged into slope-intercept form as well. Starting from \(4y - 5x = 9\): 1. Add \(5x\) to both sides: \(4y = 5x + 9\) 2. Now, divide by 4: \(y = \frac{5}{4}x + \frac{9}{4}\) Now we have two equations: 1. \(y = \frac{4}{5}x - 2\) 2. \(y = \frac{5}{4}x + \frac{9}{4}\) Next, we can compare their slopes. The slope of the first line is \(\frac{4}{5}\) and the slope of the second line is \(\frac{5}{4}\). Since the slopes are different, the lines will intersect at exactly one point, which means the system has one unique solution. Thus, the number of solutions the system has is **one solution**.