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Solving Systems using Matrices - Concept

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

A system of equations is two or more equations that contain the same variables. Solving systems using matrices is one method to find the point that is a solution to both (or all) original equations. Besides solving equations using matrices, other methods of finding the solution to systems of equations include graphing, substitution and elimination.

When you're asked to solve a system of equations, you guys already know a couple of good skills, you know how to use graphing, substitution and elimination. There's still another method and that's called using matrices. And matrices are really really effective if you have more than 2 equations and 2 variables. Or even more than 3 equations and 3 variables. Matrices will work for like 8 equations and 8 variables or even more than that. This is what's often used in the real world outside of the Math classroom if you can believe it.
Okay so if you know if you're able to solve a system of equations using a metrics if you have the same number of equations with the same number of variables, and we'll get back to that.
In order to solve a system of equations using matrices there's only one little product you have to remember. You're going to be taking the inverse of metrics a and multiplying it by metrics b in order to find your solutions, we'll talk more about what that means. The first thing you're going to do, step one is to organize the equations so the variables are in the same order and also the right side of your equations is equal to the constants. You only want the constants in the right side of your equal sign, cause that is going to represent metrics b. Metrics a is the coefficient metrics, here is what that means, input your coefficient metrics as metrics a. The coefficients remember are just the numbers that your variables are multiplied by.
So you input your coefficients in order as metrics a, you input your constant metrics as metrics b that's what your equations will equal to. And then from the home screen you're going to calculate the product of the inverse of a times b, that's going to tell you the solutions with the variables in order vertically.
It will make more sense once you guys start practicing this, you're going to need a graphing calculator or a computer program to do it, this is not something you can do by hand yet. You'll learn how to do a lot of these stuff by hand in your Algebra Two course but for today I'm going to show you how to solve systems of equations using matrices on the graphing calculator.

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