Solve a system of equations involving multiple algebraic transformations and calculate points of intersection using distance formulas | Step-by-Step Solution

💡 Quick Summary

I can see you're working with a system that involves linear equations in different forms - this is a great problem for practicing algebraic manipulation and understanding how different equation forms relate to each other! The key insight here is recognizing that you have equations written in point-slope form, standard form, and general form, but they all represent linear relationships. What do you think would happen if you converted all of these equations to the same form, say standard form (Ax + By = C)? Once you have them in the same format, you'll be able to see more clearly what the relationships are between these lines - are any of them actually the same line written differently, or are they truly distinct? I'd encourage you to start by taking that first equation in point-slope form and converting it step by step, then see what patterns emerge when you compare all three equations. You've got all the algebraic skills you need for this - it's really about being systematic with your transformations!