SAT Instructor Dan M. shows you a shortcut method for solving system of equations math qs on the New SAT.
Hey, guys. Dan here from Prepped and Polished. Thanks for joining us today. So on your new SAT math section, you’re going to see some systems of equation questions that can be solved a number of different ways. One way that you probably learned in school is very long, but we’re going to work on the short way to do it to save you time on your SAT.
All right, guys. So here’s a question from the new SAT math. It’s going to be on one of your no calculator sections. So what we have here is it gives us these two systems of equations and it says if (x, y) is a solution to the system of equations above, what is x minus y and it gives us our four choices. So a lot of students will either start by trying to solve for one of the variables in one of these and plug it into here or they might even start by trying to subtract this equation here from the top equation, but they’ll run into some problems there with the signs. They will never get the signs right because, remember, we’re not just looking for x or y. We want x minus y. So we really want to get this, separated all by itself.
All right. So guys, we can always solve these things by isolating a variable, plugging it back in, but it takes a long time, okay? So remember, on your SAT, there’s probably going to be some sort of shortcut especially if it’s one of those questions it’s early on in the section. So always look to see if there’s some way that you can do things a little bit simpler, a little bit quicker because it’s probably there.
So instead of isolating the variables, we could subtract them, but we’d run into some sign problems. So if I did it all that, we’d see that there’s a sign problem and we never get our x minus y. So even though you used to subtract them, sometimes it makes sense just to add them together. So what I’m going to do now is I’m going to add these two equations together and see what we get. So 2x plus 3x is 5x and a negative 3y plus a negative 2y is a negative 5y.
And then, of course, on this side, negative 14 plus a negative 6 is negative 20. So right away, you should see that we’re kind of on the right track. We have our minus here with x and y and a bell should go off right away, 5, 5, 20, they’re all divisible by 5. So let’s get rid of that. So if we divide each one of these terms by 5, we get just an x here, minus a y here, and negative 20 over 5, of course, is negative 4 and you’re done. So you can see x minus y equals negative 4. We’re done since that’s exactly what we’re looking for. Always make sure to check what you’re looking for. Some people get this and start to solve for x. Not necessary.
We already have our answer right here, it’s C, and we can circle it. So remember to always look for those shortcuts. So remember, guys, when you see your systems of equation problems on the SAT, look to do something to simplify. You could always solve for a variable, plug it back in. Don’t do that. It takes too long. Look to either add or subtract in some way in order to simplify those equations to get what you’re looking for.
All right, guys. Well, thanks for joining us today. Hope the little instructions here help you. If you ever need some tutoring or you want some help questions, go to preppedandpolished.com. And otherwise, good luck on your test.
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