Learning Resource Type

Classroom Resource

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

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.

    Unpacked Content

    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.

    Unpacked Content

    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.
    Link to Resource

    CR Resource Type

    Audio/Video

    Resource Provider

    PBS
    Accessibility

    Accessibility

    Video resources: includes closed captioning or subtitles
    License

    License Type

    Custom
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