Find a System Remix

This is a remix of the lesson "Find A System" by Illustrative Mathematics (https://goopenva.org/courses/a-rei-find-a-system/view). 

The original lesson has students find a system, without graphing,  where (−2,3) is a solution to the first equation but not to the second equation, and where (5,−2) is a solution to your system. Students then graph to prove that they are correct. 

I think this could make a good introduction to systems of equations. I would have students find an equation where (-2, 3) and (5, -2) were both solutions. I would have them prove it algebraically and graphically. I would then have them find an equation where (-2, 3) is not a solution and (5, -2) was a solution. Again, they should prove it algebraically and graphically on the same plane as the previous equation. I would then have them make observations about the two graph and have them say how they can tell (5, -2) is a solution the system.