I'm trying to solve some problems for a homework assignment and I'm a bit confused. For each question, they want me to determine if the equations are NOT a linear system and why. They are formatted like this:

-2x + 3y = 7.5

7x - 2y = -2.5

They want me to compare the equations and determine if they represent a linear system. I know how to do this when coordinates are given for x and y, but I'm not sure how to go about this when the variables x and y are unknown. Can someone help?

What you mean to say if the given coordinates are the solution, then you know how to do this (although I disagree with that). If I give you any random point or even a point on one of the lines you can tell me if the equations are a linear system? Even if I give you a point that satisfies both equations, then you can tell me if you have a linear system? I am sorry but this is not true.

First, can you please tell me what a linear system is?

2nd: If you randomly draw two lines on your paper, please tell me exactly how many places that may intersect?

3rd: Can two parallel lines intersect? If yes, then in how many places? Can you describe the places where they intersect.

As soon as you answer these questions you will be given further assistance. Thank you