1. \( 4 x-5 y=-20 \) and \( 2 x+y=4 \) 2. \( 2 x-3 y=2 \) and \( 5 x+y=5 \) 3. \( x+3 y=12 \) and \( 2 x+y=9 \) 4. \( 3 x-5 y=4 \) and \( 2 x-3 y=7 \) 5. \( 2 x-3 y=12 \) and \( x+2 y=6 \)

Let's dive into the equations! 1. Did you know that linear equations in two variables, like the ones you're working with, form a straight line when graphed? The point where two lines intersect represents the solution to the system—essentially the values of \( x \) and \( y \) that satisfy both equations simultaneously. It’s like finding the perfect spot to pitch a tent between two friends who can’t agree on a location! 2. Solving these systems can be done using various methods—substitution, elimination, or even graphical methods. A common mistake is forgetting to double-check your arithmetic when combining equations or isolating variables. This can lead to incorrect solutions. So, always take a moment to review; your future self will thank you for the clarity!