Lesson Plan: Solving Systems of Equations Graphically | Nagwa Lesson Plan: Solving Systems of Equations Graphically | Nagwa

Lesson Plan: Solving Systems of Equations Graphically Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to solve a system of two linear equations or one linear and one quadratic equation by considering their graphs and identifying the point of intersection.

Objectives

Students will be able to

  • understand that the solution set of a system of equations is graphically represented by the point or points at which the lines intersect,
  • understand the possible solution cases that arise when solving a linear–quadratic system of equations by using the discriminant, specifically,
    • if 𝑏4𝑎𝑐>0, then the system has two solutions,
    • if 𝑏4𝑎𝑐=0, then the system has one solution,
    • if 𝑏4𝑎𝑐<0, then the system has no solution,
  • draw the graphs for systems of two linear equations or one linear and one quadratic equation, solve them by finding the points of intersection, and verify the solutions using substitution,
  • solve real-world applications of systems of equations.

Prerequisites

Students should already be familiar with

  • solving linear and linear–quadratic systems of equations algebraically,
  • graphing linear and quadratic functions.

Exclusions

Students will not cover

  • systems of equations involving more than 2 variables,
  • systems of quadratic equations.

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