Hi there! Well the thing is, what the number is solutions is referring to is the number of times that these two lines cross. Imagine two pieces of uncooked spaghetti (but they have no ends and go on forever). If you set them down you could make them cross once in tons of different ways. You could also make them never cross by laying them parallel to each other. Or you could make them always cross by putting one on top of the other one. This method algebraically figured out which situation we have so that you don’t need to graph them. Graphing is an inefficient way to figure this out and always has a lot of room for error. Understanding how the slope of lines determines this is where you want to really focus. Same slope for both lines means parallel or on top of each, so hence no solution since parallel or infinitely many if it is just the same line one on top of the other. One solution then occurs anytime they have different slopes, or the angle which you lay down the spaghetti is a different angle. Even if the two do not cross the way you lay them down, if they extended forever at the ends they would cross somewhere, even if it is outside your house down the street or in another state, eventually they would cross. This fundamental understand if the WHY is how you really understand math. This whole situation doesn’t even make any sense for one line. Because one piece of spaghetti can’t cross or intercept with another if there isn’t a second piece. I imagine you are looking at a different type of problem. In the near future, I do plan to create some short videos teaching some of these concepts, so please share the problem here! I have some guesses as to the type of problem, but it wouldn’t be 1, none, or infinitely many, so I would like to hear what the problem is and give you a little guidance.
Finding solutions to liner equations using graph, "please". Thank you!
how do you do the same thing (figuring out if it is one, no, infinite) but with one equation???
Hi there! Well the thing is, what the number is solutions is referring to is the number of times that these two lines cross.
Imagine two pieces of uncooked spaghetti (but they have no ends and go on forever). If you set them down you could make them cross once in tons of different ways. You could also make them never cross by laying them parallel to each other. Or you could make them always cross by putting one on top of the other one. This method algebraically figured out which situation we have so that you don’t need to graph them. Graphing is an inefficient way to figure this out and always has a lot of room for error. Understanding how the slope of lines determines this is where you want to really focus. Same slope for both lines means parallel or on top of each, so hence no solution since parallel or infinitely many if it is just the same line one on top of the other. One solution then occurs anytime they have different slopes, or the angle which you lay down the spaghetti is a different angle. Even if the two do not cross the way you lay them down, if they extended forever at the ends they would cross somewhere, even if it is outside your house down the street or in another state, eventually they would cross. This fundamental understand if the WHY is how you really understand math.
This whole situation doesn’t even make any sense for one line. Because one piece of spaghetti can’t cross or intercept with another if there isn’t a second piece. I imagine you are looking at a different type of problem. In the near future, I do plan to create some short videos teaching some of these concepts, so please share the problem here! I have some guesses as to the type of problem, but it wouldn’t be 1, none, or infinitely many, so I would like to hear what the problem is and give you a little guidance.
How did you know I’m not watching in full screen
How dare you!!! 🤣
OK I subscribed to make up for not watching full screen .