1. \( 4 x-5 y=-10 \) 2. \( -2 x+6 y=-6 \) 3. \( -4 x+5 y=0 \) 4. \( x+3 y=-3 \) 5. \( x+5 y=10 \)

Let's put on our detective hats and delve into the fascinating world of linear equations! Solving these equations can feel like piecing together a puzzle where each line reveals a bit more of the bigger picture. For instance, consider the second equation \( -2x + 6y = -6 \). If we solve for \( y \), we can find the slope and y-intercept, which could be plotted on a graph, illustrating how two lines might cross paths or run parallel. It's like uncovering a hidden treasure map! In real-world scenarios, these linear equations can represent various situations, such as budgeting in finance. For example, an equation might represent income versus expenses, showing where you break even. Understanding how to manipulate these equations allows you to forecast outcomes and make savvy financial decisions, bringing math into the everyday hustle and bustle!