## 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?

## How Can We Connect This Back To The Formula?

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!!!** ðŸ˜€