Explanation for Question 21 From the Math (Calc) Section on the 2019 March Sat
Question 21 says which ordered pair is a solution to the system of 2 equations above. So first what I'm going to do is I'm going to take 3 this top equation and I'm going to isolate Y then I can take that 4 and plug it into the bottom equation. So I'm going to add Y to 5 both sides and subtract one. And that gives me, 6 oops, that gives me Y is equal to, 7 uh, X minus one. 8 So now I can take that and plug that into this bottom equation. 9 And that way there's only going to be one variable, 10 which is ax, and then we can solve for X. So this becomes X 11 plus X minus one is equal to X squared minus 12 three. And when that's all on one side, 13 it becomes X squared, minus two X minus two 14 is equal to zero. Now I'm not going to try to factor this normally, 15 because I noticed that all of the answer choices have radicals in them, 16 which means I'm probably going to need to use the quadratic equation to do 17 this. 18 So I'm going to start by doing that. So opposite of B is opposite 19 of negative two, which is just positive two plus or minus root, 20 which is, uh, two squared or negative two squared, 21 which is four plus or sorry, 22 minus four times a, 23 which is just one times C, 24 which is negative two. So that's why I wrote a plus sign here all 25 over two a, which is just two. And this becomes two 26 plus or minus route 12 over two. 27 Now route 12 is equal to route four times three. 28 So I can actually simplify this to two plus or minus route four, 29 which is just two times three, 30 all over two. And then when I divide everything by two, 31 it becomes one plus or minus root three. 32 And there's actually only one answer choice that has one plus three or one 33 minus root three is the X value. And that's a, 34 which has one plus root three as the X value. 35 So since that's the case, we don't actually have to solve for the Y 36 value. We just know that a is the price.