[Video] Q28: If the system of inequalities y > 2x +1 and y > 1/2 x -1 is graphed in the xy-plane above, which quadrant contains no solutions to the system?

Explanation for Question 28 From the Math (Calc) Section on the Official Sat Practice Test 1

So now we're looking at question number 28, which says that in the system 2 of any qualities, blank and blank is grafted in the plane, 3 which quadrant contains no solutions. 4 Right? So we're looking for the quadrant that is not in our solution range. 5 And we can start by just grabbing these. That's going to be the most 6 simple and easiest way to actually read our answers. 7 Right? So we start at plus one, 8 and then from there we go up to over two, 9 up to over two. So we have a line that looks maybe not right 10 there. We have a line that would look kind of like this, 11 right? And we want Y to be greater than or equal to that line. 12 So we're going to shade the above part for greater. 13 So we know right away that one, three or one, 14 two and three are possible answers, but four is not going to be necessarily 15 in our solution, at least for this line. So now let's graph this one, 16 this one, we start at negative one, and then we have a slope of 17 one, half the slope of one half. 18 So it's a slower slope, but they'll intersect eventually. 19 So we're right here. Right? And we also want Y to be greater. 20 We want Y to be greater. And so what we're really looking for here 21 is where these two sections overlapped and we can see that they overlap from 22 here on up. Right. And the only thing that's not in that overlap is 23 going to be quadrant four. Right? 24 Cause three is in the overlap just in its corner, 25 right about here. Two has a lot in the overlap. 26 I know it's hard to see now through all the writing, but two is 27 right here. And then one also has a lot in the overlap. 28 Four has a little bit just from this line, 29 but the key is that we need both of the, 30 both of the regions to overlap, to give us our answer choice. 31 Right? So even though this equation has a little bit in four, 32 it lacks from this equation. And so that's why C quadrant four is going 33 to be our correct answer.