Everyone. So let's take a look at this example problem we're working out together. We've got these three graphs that are showing these three pairs of lines, and we want to take these graphs and match them to their system of equations shown here below. So, really, I'm going to just try to match equations to graphs. Let's take a look at the first one over here because I've got y=3x+5 and y=-2x+10. Notice how both of these are in slope-intercept form. So it's going to be a little easier to sort of try to match the equation with the graph than, for example, this equation, which is a little messier. Alright? So let's take a look at this 3x+5. I'm looking for something that crosses the y-axis here at positive 5. So let's take a look at this first graph over here. I'm looking to see if anything crosses at y=5, and it actually doesn't. So neither of these two graphs do. What about this one? In fact, both of these actually cross at y=10 or y-intercept of 10. And over here, what I see is that the red equation does actually cross the axis at y-intercept 5. Alright? But let's just double-check the next equation, where this says y=-2x+10. So now I'm looking for a y-intercept of positive 10. Remember, this is like y=mx+b. Looking for the b term, which is 10. And if you look here, the blue equation does actually cross here at y=10. So that means that this is probably the equation or the graph C over here that I'm looking at. But just to sort of triple-check, what we're going to do here is we're going to look at this intersection point, and we're going to plug it into both of these equations here. So remember, we're just going to take a look here, and we're going to plug these x and y values into their equations and see if we get true statements for both of them. Alright? So if you bring this equation down, what this says is that 8 is equal to 3×1+5, and 8 does in fact equal 3+5, so you just get 8 equals 8, which is a true statement. If you do it for the bottom equation, for the blue equation, what you'll see is you're going to get 8 equals -2×1+10, and 8 does in fact equal negative two plus 10 because that equals 8 as well. So this is definitely going to be a true statement. Alright? So let's take a look at now the second equation or second pair of equations. I've got y=4x+8. So if you look through my graphs, what you're looking for is remember, this is going to be in slope-intercept form. So I'm looking for something that crosses the axis at a positive 8. So does anything cross the axis at positive 8? It actually does over here, so that might actually be the answer. But let's take a look at the second graph over here just to kind of make sure. In fact, what we actually said here for graph B is that both of the lines cross at a y-intercept of 10. So because of that, this definitely can't be the right answer. And, in fact, this one is going to be A. Alright? Now you can go ahead and pause the video if you want to and just double-check that this intersection point is going to work for both these equations. But you will see that if you plug in the values of, like, for example, negative 14, if you plug them into both of these equations, you will get true statements for both. Feel free to pause and sure to check that yourself. And that just means that by default, this equation 3 is going to line up with graph B because both of these things have a y-intercept of 10. And in fact, what you can actually see here is if I sort of rearrange this equation, this actually becomes y=-3x+10, and this equation over here becomes y=x+10. Notice how both of them have a y-intercept of 10, so that lines up with these two graphs over here. These are the red and blue lines. Alright? So that's the answer to this problem. Hopefully, that made sense. Thanks for watching.