OK, I get it – here is a snapshot of what I saw along with my comments on the work:

Upon closer inspection, I saw that the only real error in the student’s work was a sign error in solving the second equation for y. She wanted to have the two equations in the familiar form y=mx+b, and then find three points for each line. That was her method – and if she hadn’t made that one error, her solution would have been completely correct. I was thinking “Gee, if she were lazy like me, she would not have first manipulated the given equations into slope/intercept form, maybe not made that mistake, and then would have had the correct graph and solution.” But for what she did, her solution was actually correct.

So, now as I think about it, I see that this student is actually a great lazy mathematician – she has a method that works for her – she can’t use extra energy to apply different methods for each situation – she can find a solution quite nicely, thank you, just doing it her way. And I should not have a problem with that – she found some points that were on each line – plotted those points – drew the lines – and gave her answer.

Then I noticed that she used the same x values for each line – WOW! What a great economy of time that works out to be – she doesn’t need to try and think of x values that give nice y values – she is happy to just plug away and plot points. Nice.