Most obvious way to trick my students with system of equations

so here's one of the most obvious ways that students get mixed up on a problem like this and what they do is they just go and apply like either elimination without looking at if the variables are going to be aligned now if you're doing substitution that's a little bit different story because you're just isolated in a variable and then plugging it into the other equation but I only like to do substitution when I already have a variable isolated and you can see in this case we don't have that so what I'm going to want to do is use the elimination method now you can recognize here that in my top equation I have you know 2x plus 3y equals 7 but in my bottom equation I have a 5y minus 1 equals 2x right so they're not aligned and remember when you're applying elimination you're either just adding or subtracting two equations vertically so there's no one way to have them like perfectly aligned or like the perfect way should X and then y or should do y and then X but a kind of like a general rule of thumb is just to kind of follow the standard form and again this is not a perfect solution for everything but I think in this equation you can see that the top equation is in that standard form so what I'm going to do is I'm going to go ahead and rewrite my bottom equation so therefore it can be in that format now to do that what I'm simply going to need to do is subtract the 2x on both sides as well as add the 1 to both sides okay so now you can see what I have is everything vertically aligned and that's really important because in this case this problem is actually really really simple right it's very obvious a lot of students will make this mistake because they won't think or maybe there's a time sensitive test going on and you know it's kind of like one of those like mental farts that go on and we're like oh crap you know what am I doing like let's quickly do this and they sometimes just over Overlook it or they forget it it's one important thing that I really really want you to make sure you're paying attention to especially when you're doing elimination is make sure everything is vertically aligned and if it's not vertically aligned like it's not bad it's not hard to go ahead and rearrange it but it's essential for you to be able to do that and the nice thing that's really important about this is do you notice that my exes already like set up perfectly for elimination right I have the exact same coefficient for my X once positive and one's negative so therefore in this equation I can simply just add these two equations up vertically so 2x minus a 2X is going to be a 0x which is just 0. 3y plus a 5y is going to be an 8y and 7 plus 1 is going to equal an eight now I can just divide by eight on both sides and Y is equal to one now remember we still need to finish this equation and in this example it doesn't really matter which equation we're going to plug in for y I will say this probably this top equation before I actually had to manipulate it was probably not too bad to go ahead and plug in you know a one and two to go ahead and solve for I'm sorry to solve for x right because I already have this x almost all by itself so all I simply need to do is plug in the 1 in for the Y and now all I simply need to do is go ahead and simplify this to go ahead and solve for y and there you go once you have everything aligned you're all set to go ahead and solve for x as well as to solve for y