SLE - Systems of Linear Equations (Overview)
Linear Equations and Inequalities
Introduction
In this module we will continue our study of linear equations, except we will study two equations at one time! Think about the different cell phone plans studied last module. Imagine you have to decide between one plan that costs $25 a month and $0.10 a minute, but there is another plan that costs $15 a month and $0.16 a minute. So you have to consider how many minutes a month you talk on the phone and determine which plan would be most cost effective for you. We want to be able to compare two functions to determine when and if they intersect and what that tells us in the context of our problem.
Essential Questions
- How do I compare two linear functions given different representations?
- How do I solve a system of linear equations graphically?
- How do I solve a system of equations using substitution?
- How do I prove that a system of two equations in two variables can be solved by multiplying and adding to produce a system with the same solutions?
- How do I interpret the solution of a system of equations in the context of my problem?
Key Terms
The following key terms will help you understand the content in this module.
Linear Function - A function with a constant rate of change and a straight line graph.
Linear Model - A linear function representing real-world phenomena. The model also represents patterns found in graphs and/or data.
Ordered Pair - A pair of numbers, (x, y), that indicates the position of a point on a Cartesian plane.
Slope - The ratio of the vertical and horizontal changes between two points on a surface or a line.
Substitution - To replace one element of a mathematical equation or expression with another.
X-Intercept - The point where a line meets or crosses the x - axis.
Y-Intercept - The point where a line meets or crosses the y - axis.
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