Is \( (3,2) \) a solution to the system \( y-x=1 \) and \( -3 x-2 y=5 \) ? No, because \( (3,2) \) is a solution to only one equation. No, because \( (3,2) \) is a solution to neither equation. Yes, because \( (3,2) \) is a solution to one equation. Yes, because \( (3,2) \) is a solution to both equations.

To determine whether \( (3,2) \) is a solution to the system, we need to substitute \( x = 3 \) and \( y = 2 \) into both equations. For the first equation \( y - x = 1 \): substituting gives \( 2 - 3 = -1 \), which is not true. For the second equation \( -3x - 2y = 5 \): substituting gives \( -3(3) - 2(2) = -9 - 4 = -13 \), which also doesn’t equal 5. Therefore, the point \( (3,2) \) is indeed a solution to neither equation. Being able to effectively solve systems of equations is super handy in various real-world situations. Think about it! Whether you're balancing a budget, planning the best route for delivery, or even figuring out your workout routine, systems of equations help you make decisions based on multiple conditions or constraints. It’s like being a detective, piecing together clues to find the best outcome!