# SOLUTION to Systems of Equations GRAPHS

## Algebra 1

Hey, class, this is miss champagne, and today I'm going to teach you about lines that intersect and where they intersect is called the solution. So we have Y equals four X plus three. Of course you know this is in Y equals slope, Y intercept form. So we look to see which line touches at the positive three, and that will be the line for this equation. So I see a positive three here. So I know that this line matches this equation. So I'm going to draw an hour from this line to this equation. Here Y equals negative X minus two. I'm looking to see which graph touches the Y axis at negative two. I see negative two, this line touches at negative two. Therefore, this is the line for this equation. And it also makes sense because the slope is negative, which means that it's pointing towards the left. These two lines touch or intersect. Intersect means touch. These two lines intersect here, and this number is called let's get a closer look. If we start here, and we drive over, we drive over to a negative one. So they touch at negative one, and then I go down to negative one. Negative one. So this means that X equals negative one, Y equals negative one. X, the X number is called the domain, the Y number is called the range. Is also called the input and the output, it's also called the independent variable. So your Y is called the dependent variable. The negative one and the one together, we call a relation. So the answer is the solution is X equals negative one. Y equals negative one. Or negative one, comma one. This is called your relation. Your point, your ordered pair, you can also call it the coordinate. So all of these are vocabulary words that mean negative one comma one. If we look on the back, we will see if you see two lines that do not intersect. They do not intersect, that means they do not touch. This is called a parallel line. Which has no solution or no point at which they touch.