It would not have occurred to me that these mistakes are related, except insofar they indicate a complete lack o understanding of the equals sign, the constant term, or multiplication (so, linear equations). I’m anxious to read whether anyone thinks they might be.

I can’t figure out why the student got y=3x on the first problem. Show more work!!

For the second problem, I think the student doesn’t know which is x and y in the coordinates (3,2) and so “covers his/her bases” by saying “if x is this, then this is the answer” and tries both (3,2) and (2,3). I think the student does know how to solve 1 and 2-step equations because those b’s are correct for the points (3,2) and (2,3).

I don’t know if it is reasonable to assume this but it seems like the student took the coefficients and constant in #18 and tried to rearrange them into an equation that could still be equal. You can substitute the numbers as they wrote them into their equation and get a true statement.

Perhaps the big idea that’s missing is the idea of using inverse operations to generate equivalent equations. They may be able to do this with one variable but not two variable if they learned that the point of using inverse operations is to solve for “the” variable. A student who learned the inverse operations as a set of steps for one variable equations may have a lot of difficulty generalizing them to two variable equations.