Determine if the following system of equations has no solutions, infinitely many solutions exactly one solution. \[ \begin{aligned}-6 x+5 y & =-9 \\ -11 x+10 y & =-17\end{aligned} \]

To analyze the system, we can check if the two equations represent parallel lines, which would indicate no solutions, or the same line, which would imply infinitely many solutions. First, we can express both in slope-intercept form (y = mx + b): 1. For the first equation: \(-6x + 5y = -9 \implies 5y = 6x - 9 \implies y = \frac{6}{5}x - \frac{9}{5}\) Here, the slope (m1) = \(\frac{6}{5}\). 2. For the second equation: \(-11x + 10y = -17 \implies 10y = 11x - 17 \implies y = \frac{11}{10}x - \frac{17}{10}\) Here, the slope (m2) = \(\frac{11}{10}\). Since the slopes (\(\frac{6}{5}\) and \(\frac{11}{10}\)) are different, the lines intersect at exactly one point, hence the system has exactly one solution. For a sneak peek into solving systems, always look for an easy way out: try simplifying first, or graphing just to catch that solution visually! And don’t forget, when two lines share the exact slopes and intercepts, they’re party pals with infinitely many solutions!