Learning Resource Type

Classroom Resource

Solving Systems of Equations

Subject Area

Mathematics

Grade(s)

8

Overview

In this video lesson, students continue to explore systems where the equations are both of the form y=mx+b. They connect algebraic and graphical representations of systems, first by matching graphs to systems, then by drawing their own graphs from given systems. Additionally, students see how to see the number of solutions from both the graphical and algebraic representations. Then they examine other types of systems with different structures and use the structure of a system of equations to reason about its lack of solutions. When students look at the structure of a system before starting to solve it in order to develop a good approach to solving, they engage in MP7.

Grade 8, Episode 5: Unit 4, Lessons 13 & 14 | Illustrative Math

    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
    License

    License Type

    Custom
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