Using the Substitution Method to Solve Systems of Linear Equations | Algebra 1: Module 5: Topic 7

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

8

Overview

In this program, students learn the method of solving by substitution, which works by solving one of the equations, you choose which one, for one of the variables, you choose which one, and then plugging this back into the other equation, substituting for the chosen variable and solving for the other. Then you back-solve for the first variable. 

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
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