Real Life Phenomena Explored Through Systems of Linear Equations Overview

Introduction

In this module, we will explore systems of linear equations. We will look at graphs and approximate the solution of two linear equations in two variables by inspecting the graph and using the point of intersection. We will also see how systems of equations can help us solve all types of real-world problems where linear equations can be derived. We will learn about different methods for solving systems algebraically to find exact solutions. We will also compare equations of systems that are either parallel to each other, lie on the same line, or intersect at one point.

Essential Questions

What are the different ways to solve systems of linear equations?
What does the solution to a system mean graphically and algebraically?
How do I determine if a system of linear equations has one, infinite, or no solutions?
How can systems of equations be used to represent situations and solve problems?

Key Terms

The following key terms will help you understand the content in this module.

system of linear equations - Two or more equations that together define a relationship between variables.

simultaneous equations - Another name for a system of Linear Equations.

solution of a system - the points (x,y) at which both lines that represent a system intersect

ordered pair - a pair of numbers that give the coordinate of a point on a grid in this order: (horizontal x, Vertical y)

no solution - in a system of linear equations this means the lines are parallel

infinite solution – In a system of linear equations, this means the lines are colinear for both equations.

substitution method - one equation is solved for one variable and that solution is substituted int the second equation

collinear - the line is the same, points lie on the same line

elimination method – adding, subtracting or multiplying a system of equations to help solve a system

graphing method - graphing 2 or more linear equations to determine the solution to the system

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