Let's try another example. Graph the solution set. We have a system of linear inequalities. The first inequality is 3x + 4y is greater than 12. The second inequality, y is less than 3/4x - 1. Let's take a look at this first inequality, 3x + 4y is greater than 12. And we want to graph the solution set of that individual inequality. To do that, we'll solve the inequality for y. And to do that, we'll start by subtracting 3x from each side of the inequality. That gives us 4y by itself on the left. On the right, 12 - 3x can be written as -3x + 12. And now we're going to divide each side of our inequality by 4. And when we do that, we get y by itself on the left. On the right, -3x over 4 can be written as -3/4x, plus 12 divided by 4, which is 3. So we're going to now replace our inequality symbol with an equals sign. And that equation gives us the equation of our boundary line. And that will be a line with a slope of -3/4 and a y-intercept of (0, 3). So let's get our rectangular coordinate system and draw this line. And we will start by plotting our y-intercept at (0, 3), 3 units up the y-axis. Our slope is -3/4, so let's go down 3 and to the right 4 to get another point on our line. Notice that we have a strict inequality. y is greater than -3/4x + 3. So equality is not allowed. That means the points on our boundary line are not a part of our solution set. And again we will indicate that by drawing a dashed line through those points. And since we have y is greater than -3/4x + 3, we want the ordered pairs where the y-coordinate is bigger than -3/4 times the x-coordinate plus 3. That means we're going to shade above this boundary line, so let's do that. And that is the graph of the solution set of the first inequality. Let's take a look at our second inequality, which is already solved for y. y is less than 3/4x - 1. Let's draw the boundary line given by the equation y = 3/4x - 1. That would be aligned with the slope of 3/4 and a y-intercept of (0, -1). So we're going to plot our y-intercept at that point, one unit below the x-axis (0,-1). Our slope is 3/4, so we can go up 3 and to the right 4 to get to another point on our line. Again, equality here is not allowed. We have a strict inequality, so once again we're going to draw a dashed boundary line. And notice that we have y is less than 3/4x - 1, so we're going to shade in below this boundary line. And notice that we can see where these two solution sets intersect: that green region there. So let's finish shading this in. And we can see the solution set to the system of linear inequalities. It's that green region, the intersection of the solution sets of the two individual inequalities. Let's try one more example. And in this last example we want to graph the solution sets of the system of linear inequalities, where the first inequality is 2x + 3y is greater than 9. The second inequality is y is less than -2/3x + 1. So again, we'll start with our first inequality, 2x + 3y is greater than 9. To graph the solution set of this inequality, we will solve this inequality for y. And to do that, we will subtract 2x from each side. That gives us 3y by itself on the left, and 9 - 2x, or -2x + 9, on the right. Now let's divide each side of our inequality by 3. And that will give us y by itself on the left. We have that y is greater than -2x over 3, which we can write as -2/3x, plus 9 over 3, which is 3. Our boundary line is given by the equation y = -2/3x + 3. That's a line with the slope of -2/3 and a y-intercept of (0, 3). So let's draw that line on our rectangular coordinate system. Our y-intercept is 3 units up the y-axis at (0, 3). Our slope is -2/3, so we can go down 2 and to the right 3 to get to another point on our line. Notice here that equality is not allowed. We have that y is strictly greater than -2/3x + 3. So we're going to have a dashed boundary line, as the points on our line are not a part of the solution set. And since we have y is greater than -2/3x + 3, we're going to shade in above our line. So let's do that. And now let's turn our attention to our second inequality, which is y is less than -2/3x + 1. The boundary line is given by the equation y = -2/3x + 1. The slope of this line is also -2/3; different y-intercept, however. The y-intercept is (0, 1), so we can plot that point at (0, 1), one unit above the x-axis on the y-axis. And our slope being -2/3, we can go down 2 and to the right 3 to get to a new point on our line. Again we see that equality is not allowed. And so we're going to draw a dashed boundary line again. And to determine if we are going to be above or below, we look at our inequality when we've solved it for y. It was given to us solved for y. We have y is less than -2/3x + 1. So we're going to shade in below that boundary line. And when we do that, we see that these two solution sets do not intersect at all. So that tells us that the solution set of the system is the empty set. There are no points, no ordered pairs, that make both of these inequalities true at the same time.