Explanation for Question 36 From the Math (Calc) Section on the Official Sat Practice Test 10
Now we're told in number 36, 2 that we have two equations here and that they have one solution, 3 right? So when we're talking about two equations, 4 one solution, this is really a system of equations problem. 5 Right? So if it's assistance of equations problem, 6 you could perhaps think about using substitution, 7 taking this Y and plugging it in there. 8 Right? So why is actually equal to C? So I can rewrite this bottom 9 equation saying that C instead of Y is equal to negative X 10 squared plus five X, 11 right? And so we're trying to figure out where is this X value we 12 essentially want to solve for X, but in order to do that, 13 I need to have a real functioning quadratic equation. 14 So I'll subtract C from both sides. I can get everything on one side 15 of my equation. And then this negative Outfront makes things a little more difficult. 16 So you might as well divide everything by negative one as well, 17 just for the sake of getting rid of this negative, 18 because it's easier to work with. You don't necessarily need to, 19 but it's simply easier. So X squared now, 20 minus five X plus C, we've just switched all the signs around. 21 And so we're told that we intersected exactly one point. 22 And so we're trying to figure out where is that point? 23 And the way to do that usually is once we have this to solve 24 for the X values by factoring, 25 but we're told that we have one point and whenever you factor, 26 you get two points. So that is really a, 27 um, a hint t...