Everyone, let's get started with this example problem here. So we're going to graph this system of equations that's given to us below because we're trying to identify what the intersection point is. So, basically, we have to figure out where these lines will cross each other. In order to do that, we have to actually graph them. So let's go ahead and get started here. So y=2x+3, notice how both of these equations are already in slope-intercept form. We have y=mx+b, y=something. Right? So 2x+3, what does that look like? Well, it passes through the point (0, 3) and it has a slope of positive 2. Remember, positive 2 means it's going to go up 2 and then over 1, so I'm going to put a point here, or we can go down 2 and to the left one. So if you connect these dots with a line, what you'll see is that this graph should look something like this. Alright? So that's the equation or that's the graph, y=2x+3. Let's do the same thing now for the red equation, which should be a little simpler because it's just x+4. That means that it has a y-intercept of (0, 4). And instead of a slope of 2, it has a slope of 1. So what I'm going to do now is, a slope of 1 means up 1 over 1, down 1 over 1. So it's going to look a little different. And if you sort of draw the line that connects these points, it should look something like that. It should look something like that. So that's the equation y=x+4. So we have to identify what the intersection point is. It's just the point where the lines cross, and clearly we can see these lines cross right at this point over here. The coordinates to this point are (1, 5). Alright? So with these two lines over here, the intersection is just going to be the point (1, 5). Are we done yet? Well, not quite because the rest of the problem says that we have to take this intersection point, and we have to verify that it's a solution to both equations. So what does that mean? Well, when we did this for one single equation, we would plug in the x and y values. We'd take those, and we would plug them into the equation to figure out if we got a true statement. It's the same idea here. We're just going to take these x and y coordinates, and we're going to plug them into both of the equations. We have to get a true statement for both of them, then we can say it's a solution to both equations. Alright? So it's pretty straightforward. What I'm going to do here is I'm just going to rewrite y=2x+3. And remember, what I'm going to do here is I'm just going to take these x and y values, the 5, and I'm going to plug that in for y. I'll take the 1, and replace that in for x, and then we'll solve this equation here. Alright? So we'll see what happens. So we get yisequalto2times1+3. Alright? Now you can see pretty clearly here that the left and right sides will be the same. You'll just get a statement that just says 5=5 on the left and right sides, and that is a true statement. 5 does equal 5. So this is a solution. Now we'll just do the same exact thing with the red equation, y=x+4. Do the same thing, so we're just going to replace y with 5 and x with 1, and you'll get that 5=1+4. And just like above, we'll just get a true statement. 5 does equal 5. So because this point over here, (1, 5), when you plug it into both equations, you just get true statements for both of them, 5=5, we can say conclusively that this point is a solution to both equations. Alright? Thanks for watching.