When Will We Need This?

In grade 10, our first unit is solving a system of linear equations. Also, you must understand how to solve linear equations for success in the course. Furthermore, we are taught three different methods: Elimination, Substitution, and Graphing. However, some of these methods can be very time consuming. Hence, I set out on a journey to try and find the best and fastest way to solve these problems. First, I tried to understand what our equation, y = mx + b, really meant. Then, I explored how we ended up getting to a POI. After doing all of these steps, I ended up with this: x = (b2 – b1) / (m1 – m2) where x is the x value of the POI. Now, this may seem confusing, but in reality this works like a charm. So, let’s first try this technique with a problem. After, I will show you exactly what I did to get to this solution.

A Test Problem:

Your problem is: “Find the point of intersection for y = 8x + 20 and y = 10x + 10.” Well, x = (b2 – b1) / (m1 – m2), so let’s plug in the values. x = (20 – 10) / (10 – 8) = 10 / 2 = 5. If x is 5, y = 8(5) + 20 = 40 + 20 = 60. Therefore, the POI would be (5, 60). More importantly, using this method, a problem can be solved in under 5 seconds! Now, let me walk you through how I got to this point. On another note, I have also created a function (using code) to factorize quadratic equations for us, which makes doing math homework much more efficient, just in case if you wanted to check that out.

How Do We Derive This Formula?

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How Can We Connect This Back To The Formula?

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Also, if you would like to learn by graphing some of these equations yourself, I would definitely recommend checking out desmos, where you can graph and visualize your data, which will allow you to get a better understanding of these equations and how we are actually finding the point of intersection. Not to mention, check out Khan Academy, as they have a plethora of great articles, posts and videos… explaining a wide variety of both subjects and topics.

To summarize, this is a very useful formula and I do hope that you both share this with your friends, parents and teachers, and leave a nice rating!!! 😀