If the system of inequalities y is greater than or equal to two x plus one, and y is greater than one half x minus one is graphed in the xy plane above, which quadrant contains no solutions to the system. Okay, and here are our answer choices. All right, let's take a look, which contained no solutions to the system. So when it says that no solutions to both systems, meaning that the no quadrant has x and y values that satisfy both inequalities, it could satisfy one of them, but it doesn't satisfy both. So what you'd want to do is to go ahead and graph both inequalities, and you'll be able to see for yourself so let's graph this one right here. y is greater than or equal to x plus one.

So its y intercept is at plus one. So maybe somewhere right here, and it's a positive slope. So maybe it'll look something like Like this. Okay. And for the other inequality, why is greater than one over two x minus one that will. And you notice that because we don't have an equal sign here we'll do a dash line.

So that will be minus one intercept, so maybe somewhere around here and a dashed line. So let's do something like this. Okay. All right, so now let's just fill in the answers or the solutions to each inequality. So for the red line, the red inequality, everything above it, since y is equal to two x plus one or greater than that will shade in everything above that, right. So these everything above here includes solutions to the y is equal to greater than two x plus one.

Now for the other guy, the Y is equal was greater than one half x minus one. We also shade in everything above that. So shade shade, shade. shade, shade shade. Okay? Now what you noticed is that everywhere every quadrant that contains an overlap of basically blue shading and red shading includes answers or solutions to both inequalities.

So I'm going to do that in green. So if you look at one, where do we see this overlap? Well, we see it right here. Oh, that's not green. Oops, let me get green. Here we go.

Right here. Okay. Where do we see overlap in two? Well, all of two is overlapped. And in three, we see overlap here. Okay.

What about four? Well, there's actually not overlap before. There are answers for the y's greater than one half x minus one, but there are no solutions for the other inequalities one, therefore, the quadrant that doesn't contain solutions to both inequalities is quadrant four.