So let's do a couple of examples and try and make sense of graphing solution sets of systems of linear inequalities. So here we want to graph the solution set of the system of linear inequalities. The first inequality is y is greater than or equal to 2x - 3. And the second inequality is y is greater than -3x. Let's start with our first inequality, y is greater than or equal to 2x - 3. And to graph the solution set of this inequality, we're going to start by graphing the boundary line: y = 2x - 3. That line will have a slope of 2, which we can think of as 2 over 1. And our y-intercept is going to be the ordered pair (0, -3). So let's get our rectangular coordinate system. And we'll start by plotting our y-intercept three units down on the y-axis. That's this point here. And again, our slope is positive 2. So that's positive 2 over positive 1. That tells us how to get to another point on our line. We go up two and to the right one, and we can do that a couple of times if you'd like. Now let's draw our boundary line through these points. Notice that we have an inequality which is not strict. Its y is greater than or equal to 2x - 3. Since equality is allowed, that tells us that the points on the boundary line are part of our solution set, we'll indicate that by drawing a solid boundary line. And to determine if we are going to shade in above or below that boundary line, we look at our inequality. We have it solved for y. We want the ordered pairs where the y-coordinate is greater than or equal to 2x - 3. That means we want to be above that boundary line. So let's shade above that boundary line. And so there is the solution set of our first inequality. Let's take a look at our second inequality, y is greater than -3x. Let's replace that inequality symbol with an equals sign. That gives us the linear equation y = -3x. Let's graph that line. The slope here would be -3. We'll think of that as negative 3 over 1. And our y-intercept is going to be the origin (0, 0). So let's start by plotting our y-intercept. Again that's the origin where our axes intersect. Our slope is -3 over 1. That tells us how to get to another point on our line. We go down three units and to the right one. That puts us right there. And so let's draw a line through those points. Here we notice that our inequality is a strict inequality, meaning equality is not allowed, meaning that the points on our boundary line are not a part of our solution set. We'll indicate that by drawing a dashed boundary line. And again we will look at our inequality, solve for y, to determine if we are going to be above or below that boundary line. We want ordered pairs where the y-coordinate is greater than -3 times the x-coordinate. So again, we are going to shade in above that boundary line. Let's do that. And I'll shade in above that line in blue, and notice that when we intersect the yellow, we get green. And that green area is going to be the intersection of our two solution sets. So let's finish shading in. And once again, that green shaded region, the intersection of the solution sets of the individual inequalities is the solution set of our system of inequalities, and it makes a pretty picture as well.