Following successful completion of this lesson, students will be able to:

  • Solve systems of linear equations by graphing, elimination and/or substitution
  • Determine, by inspection of the equations, the number of solutions to the system

The above objectives correspond with the following Alabama Course of Study Objectives: CCRS 2Solve application-based problems by developing and solving systems of linear equations and inequalities..

Introduction

A system of equations is a set of two or more equations. The solution to a system of two linear equations is an ordered pair that makes both equations true.

Explore: Systems of Linear Equations

Use the link above. See how the slope and y-intercept affect the solutions to a system of equations. Explore until you find the answers to the questions below the graph.

Use what you learned from your exploration to complete the following statements about a system of two linear equations.

  1. If one of the lines has a slope = 2 and the other line is parallel to it, then the slope of the other line is _?_ How many points of intersection do parallel lines have? and the system has _?_ What must be true about the slopes of parallel lines? point(s) of intersection.



  2. If the slopes of the two lines are not equal, then the system has _?_ If lines have unequal slopes, they must intersect. point(s) of intersection.



  3. If the two equations graph the same line, then both the _?_ and the _?_ must be equal. In this case, there are infinite points of intersection because every point on the line is a point of intersection.

 

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