Is \( (0,-5) \) a solution of \( 6 x-3 y=15 ? \) Yes

To check if \( (0, -5) \) is a solution of the equation \( 6x - 3y = 15 \), we can substitute \( x = 0 \) and \( y = -5 \) into the equation. Starting with the left side: \[ 6(0) - 3(-5) = 0 + 15 = 15. \] Since the left side equals the right side, \( 15 = 15 \), \( (0, -5) \) is indeed a solution! Now, let's not stop there! If you're wondering about the implications of this solution, it's a point on the line represented by the equation \( 6x - 3y = 15 \). Graphically, when plotted, it fits neatly on the line, offering a visual sense of how changes in \( x \) and \( y \) interplay. Furthermore, understanding solutions like these can help you tackle real-world problems involving linear equations, such as budgeting, where each point could represent different expenditures against income. You'll find that mastering the art of solving equations can turn complex scenarios into manageable ones, making you a pro at handling everyday numerical conundrums!