My strategy would have been to look at the multiple choices and see that only (d) satisfies the first equation, so I’m done.

Then they start doing work that looks to me like a check of the x-value but somehow to them has something to do with continuing the solving process?

I don’t understand what the kids are thinking. So let me start at the beginning again. I see that they set the two y’s equal to each other to solve for x, but then they check by setting the y’s equal to each other (again), and never really state that they’re doing anything to find the y value of the solution. The second one is particularly mystifying: where does that extra “=1” come from? In the first one, it’s just mystifying why they picked (3,1) instead of one of the other x=3 choices. I hope that other commenters here will enlighten me!

Andy

It looks like these students are solving for their other variable and checking their answers at the same time. They seem to be dividing the answer by itself when the answers equaled each other. I think they are confused when they do not get a variable equal to a number. I would try having these students solve the second equation for why before checking their work.