Explanation for Question 18 From the Math (Calc) Section on the 2018 May Sat
Question 18 says in the system of equations above K is a constant. 2 When the equations are graphed in the X, Y plane, 3 the graphs intersect at exactly two points, 4 which of the following cannot be the value of K. 5 So what I'm going to do here is I'm going to take this bottom 6 equation, plug this in for Y and then I'm going to factor using 7 the quadratic equation and we'll get to why in a second. 8 So let's just start with that first step. So this equation becomes K X 9 plus negative X squared. Plus K is equal to one. 10 And when I move everything to the left side of the equation, 11 it becomes negative X squared, plus K X plus K. 12 Plus one is equal to zero. Now I'm going to factor using the quadratic 13 equation, but I'm not going to factor completely. 14 So I know that a is equal to negative one. 15 That's the coefficient of X squared. Then now that B is equal to K 16 the coefficient of X. And I know that C or the constant is 17 equal to K minus one. 18 And sorry, I actually miswrote this year. This should be K minus one, 19 not plus one. 20 So now that I know that I can find out what the discriminant of 21 this, uh, equate equation is. 22 And the reason that I'm doing that is because using the discriminant, 23 you can find out how many solutions in equation has. 24 So the discriminant is B squared minus four, 25 a C we don't actually need the root here. 26 So B squared minus four AC. 27 So let's see what that would be in this case. So B is K. 28 So this is K squared...