Graphing a System of Equations

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

8

Overview

Solve a number riddle by finding the point of intersection for two lines. This video focuses on finding the solution for a system of equations, they are represented as an algebraic expression and a set of linear equations that are graphed to find an intersection point.

This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers and is part of the Math at the Core: Middle School collection.

Mathematics (2019) Grade(s): 8

MA19.8.12

Solve systems of two linear equations in two variables by graphing and substitution.

UP:MA19.8.12

Vocabulary

  • System of linear equations
  • Point of intersection
  • One solution
  • No solution
  • Infinitely many solutions
  • Parallel lines
  • Slope-intercept form of a linear equation
  • Standard form of a linear equation

Knowledge

Students know:
  • The properties of operations and equality and their appropriate application.
  • Graphing techniques for linear equations (using points, using slope-intercept form, using technology).
  • Substitution techniques for algebraically finding the solution to a system of linear equations.

Skills

Students are able to:
  • generate a table from an equation.
  • Graph linear equations.
  • Identify the ordered pair for the point of intersection.
  • Explain the meaning of the point of intersection (or lack of intersection point) in context.
  • Solve a system algebraically using substitution when both equations are written in slope-intercept form or one is written in standard form and the other in slope-intercept form.

Understanding

Students understand that:
  • any point on a line when substituted into the equation of the line, makes the equation true and therefore, the intersection point of two lines must make both equations true.
  • Graphs and equations of linear relationships are different representations of the same relationships, but reveal different information useful in solving problems, and allow different solution strategies leading to the same solutions.
Mathematics (2019) Grade(s): 8 - Grade 8 Accelerated

MA19.8A.9

Solve systems of two linear equations in two variables by graphing and substitution.

UP:MA19.8A.9

Vocabulary

  • System of linear equations
  • point of intersection
  • one solution
  • no solution
  • Infinitely many solutions
  • parallel lines
  • Slope-intercept form of a linear equation
  • Standard form of a linear equation

Knowledge

Students know:
  • The properties of operations and equality and their appropriate application.
  • Graphing techniques for linear equations (using points, using slope-intercept form, using technology).
  • Substitution techniques for algebraically finding the solution to a system of linear equations.

Skills

Students are able to:
  • generate a table from an equation.
  • Graph linear equations.
  • Identify the ordered pair for the point of intersection.
  • Explain the meaning of the point of intersection ( or lack of intersection point) in context.
  • Solve a system algebraically using substitution when both equations are written in slope-intercept form or one is written in standard form and the other in slope-intercept form.

Understanding

Students understand that:
  • Any point on a line when substituted into the equation of the line, makes the equation true and therefore, the intersection point of two lines must make both equations true,
  • Graphs and equations of linear relationships are different representations of the same relationships, but reveal different information useful in solving problems, and allow different solution strategies leading to the same solutions.

CR Resource Type

Audio/Video

Resource Provider

PBS

License Type

Custom

Accessibility

Video resources: includes closed captioning or subtitles
ALSDE LOGO