Write the equations in standard form, then represent the system using an augmented matrix . 3 x + 5 y − 9 = 0 3x+5y-9=0 3 x + 5 y − 9 = 0 8 x = − 4 y + 3 8x=-4y+3 8 x = − 4 y + 3

Welcome back, everyone. In this video, we're gonna take a look at these two equations that we have over here, and we're going to represent them as a matrix. Remember, when you take a system of equations and represent it as a matrix, it's called an augmented matrix. That's what that fancy word means. So before we do that, we actually have to write the equations in standard form. So let's go ahead and do that. Standard form, remember, just means that you have the coefficients like a, b, and c, like something in front of x, y, and z. You have all that stuff first, and then you have c, which is a constant that's on the other side. That's what you have in these types of problems. And we're only just gonna focus on 2 variables, x and y. Right? So what I'm gonna do is I'm gonna make sure that I have x and y on one side of the equation and then all the constants on the other. So in other words, this equation over here just becomes 3x+5y, and then I have to move the 9 over to the other side. And when you do that, it's gonna flip sign. It's gonna be it's gonna be positive. We'll do the same thing over here. So here what I've got is I've got 8 x that's on the right left side, but then I've got negative 4 y plus 3 on the right side. So how do I get this to be in standard form? Well, if you notice, we want all the coefficients on the left side. So I've already got x over here, so now I just have to bring this y over to the other side. So what you've got here is you've got 8x, and and then now what happens is this becomes plus 4 y. So this is going to become plus 4 y over here, and this is going to equal 3 on this side. Now you have both of these things in standard form. So how do I take this, these two equations that are in standard form, and turn it into a matrix? Well, remember, all we have to do is just focus on the coefficients. With with a matrix, remember, we're just gonna write these numbers, and it's kind of already understood that there's x and y coefficients over here for these 2, and there's a little bar which represents an equal sign. And then we just have the two numbers that are on the right side. So these two numbers are the easiest because you just pull the numbers that are on the right side of the equation. That goes to the 9 and 3 that are over on the right side of the matrix. And then for these two columns over here, you just have to fill out the x and y coefficients. So if you look at these two columns over here, we've got the coefficients 38, so we just write 38. And then we've got 54, so we just write 54. That's really all there is to it. So this system or sorry. This matrix here, which is called an augmented matrix, it just represents this system of equations just in a different way. Alright? So that's how you do these types of problems. Thanks for watching. I'll see you in the next one.