When doing this kind of problem, what we want to do is we want to go ahead and graph the lines. So if we have X + 2 Y less than or equal to six, solve for Y2Y less than or equal to negative X + 6 Y less than or equal to -1 half X + 3. So we're going to go up three and we're going to go down one, right? Two, it's going to be a solid line because it was or equal to. Now to determine which side to graph on. There are a couple different ways to do it. The most conventional way is to think about choosing a point, any point. We usually do the origin if I put zero in here, and if that comes out to be a true statement, I'm going to shade on that side. So is 0 less than or equal to three? And the answer is yes. So I'm going to shade this one on this side of the line I just drew. Now, if we had chosen a point such as I don't know any point. Say we chose the point 4/4 up here. Does 4 less than or equal to negative 1/2 * 4 + 3? Is that a true statement? So is 4 less than or equal to -2 + 3 one? That's not a true statement. So we would know not to shade where that point is, and we could use the original, the original equation before we manipulated it. It will work for either the solved or the original, assuming we did our math correctly. So we know not to shade out here, not here, but down here. Now, another method that I frequently tell students is to think about the airline method or the airplane if I have Y less than or equal to the line. If you thought about putting your hands out just like an airplane and then less than would be below. So now if we just move our line to look like the line we graphed, less than is still down below and that's going to tell us which direction to shade. So we'd play airplane, we'd put our hands out and we'd move things around. If we look at the second equation, 2X plus Y, we're going to solve for Y. So we're going to subtract the 2X to the other side. So we want +6 a slope of -2 down 2 / 1, down 2 / 1, down 2 / 1. So that's this line here. Now I want Y less than or equal to that. So if I thought about putting a straight line out, less than or equal to is down. So now if I move this line to look like the one I just graphed less than or equal to is still going to be going this direction. So it would be down here if we didn't see that we can. Oops. I got a little excited there. If we didn't see that, we could test a point so it's below that red line. I love colors by the way. So if I chose a point, say 00 to test, does 0 + 2 * 0 end up being less than or equal to 60? Is less than or equal to six? That's true. So that would also show me that at this point 00, that would be on the shaded side of the equation. The next line says X greater than or equal to 0. So X greater than or equal to 0, all the X values that are positive. So if we look at this line, that's our line X = 0. I want all the greater than values. We're going to be shading off to the right, so we would have everything out here. Then the last one says Y greater than or equal to 0. So if I want Y greater than or equal to 0, I want all the positive Y values. And so if we look here, we're up here then and our final solution is where are all four of those shaded? And it's kind of messy to see now, but you can see hopefully that all four of them are shaded in this area right in here. I need all four of them to be true. So that's where all four of them would overlap.