Systems of equations

- [Voiceover] The ability to work…with Systems of Linear Equations…is an important part of Data Science.…The idea here specifically is how do you work…with many unknowns?…The problem is when there's a Mutual Dependence,…so for instance, X depends on Y but Y depends on X,…and that sounds like it can be super difficult,…but what's funny is that Systems of Linear Equations…can actually be solved by hand.…You can also use linear or matrix algebra…and I'll demonstrate both of these.…Let's use a quick example of somebody…who's making and selling iPhone cases.…

Let's say you sold a thousand cases,…some sold for 20 dollars, some sold for five,…and you had a total revenue of 5900 dollars.…How many cases were sold at each price?…Well, we're gonna write these out in equations.…The sales is equal to this,…it's x which is one price point…plus y, another price point…equals 1000 cases total.…The revenue of 5900 dollars is equal to x times 20 dollars…plus y times five dollars.…

So we have two equations here…and we have to find a way to combine them…