\begin{tabular}{|c|c|} System B \\ \( 6 x-5 y=4 \) \\ \( -6 x+5 y=5 \)\end{tabular}\( \quad \begin{array}{l}\text { The system has no solution. } \\ \text { The system has a unique solution: } \\ (x, y)=(\square, \square) \\ \text { The system has infinitely many solutions. }\end{array} \)

If we analyze the equations in this system, we can see that they represent two lines in a plane. The first equation, \(6x - 5y = 4\), can be rearranged into y-intercept form, revealing its slope and y-intercept, while the second equation, \(-6x + 5y = 5\), does the same. If the slopes are equal and the y-intercepts differ, these lines are parallel and thus have no solution—meaning they never intersect. To solve this system, we can utilize substitution or elimination. Here, either method could quickly show us that the two equations are indeed inconsistent. A good practice is to add the two equations together to see if they simplify to a contradiction, like \(0 = 9\). This reinforces that there’s no point where both equations hold true simultaneously. Remember, graphs are your friends here!