ALEX Classroom Resource

  

Solving Systems of Equations

  Classroom Resource Information  

Title:

 Solving Systems of Equations

URL:

 https://aptv.pbslearningmedia.org/resource/our20-math-841314/solving-systems-of-equations/

Content Source:

 PBS
Type: Audio/Video

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

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 8
12. Solve systems of two linear equations in two variables by graphing and substitution.

a. Explain that the solution(s) of systems of two linear equations in two variables corresponds to points of intersection on their graphs because points of intersection satisfy both equations simultaneously.

b. Interpret and justify the results of systems of two linear equations in two variables (one solution, no solution, or infinitely many solutions) when applied to real-world and mathematical problems.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Graph a system of two linear equations, recognizing that the ordered pair for the point of intersection is the x-value that will generate the given y-value for both equations.
  • Recognize that graphed lines with one point of intersection (different slopes) will have one solution, parallel lines (same slope, different y-intercepts) have no solutions, and lines that are the same (same slope, same y-intercept) will have infinitely many solutions.
  • Use substitution to solve a system, given two linear equations in slope-intercept form or one equation in standard form and one in slope-intercept form.
  • Make sense of their solutions by making connections between algebraic and graphical solutions and the context of the system of linear equations.
Teacher 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.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.8.12.1: Define variables.
M.8.12.2: Recall how to estimate.
M.8.12.3: Recall how to solve linear equations.
M.8.12.4: Demonstrate how to graph solutions to linear equations.
M.8.12.5: Recall how to graph ordered pairs on a Cartesian plane.
M.8.12.6: Recall that linear equations can have one solution (intersecting), no solution (parallel lines), or infinitely many solutions (graph is simultaneous).
M.8.12.7: Define simultaneous.
M.8.12.8: Recall how to solve linear equations.
M.8.12.9: Recall properties of operations for addition and multiplication.
M.8.12.10: Discover that the intersection of two lines on a coordinate plane is the solution to both equations.
M.8.12.11: Define point of intersection.
M.8.12.12: Recall how to solve linear equations.
M.8.12.13: Demonstrate how to graph on the Cartesian plane.
M.8.12.14: Identify ordered pairs.
M.8.12.15: Recall how to solve linear equations in two variables by using substitution.
M.8.12.16: Create a word problem from given information.
M.8.12.17: Recall how to solve linear equations.
M.8.12.18: Explain how to write an equation to solve real-world mathematical problems.

Prior Knowledge Skills:
  • Define quadrant, coordinate plane, coordinate axes (x-axis and y-axis), horizontal, vertical, and reflection.
  • Demonstrate an understanding of an extended coordinate plane.
  • Draw a four-quadrant coordinate plane.
  • Draw and extend vertical and horizontal number lines.
  • Interpret graphing points in all four quadrants of the coordinate plane in real-world situations.
  • Recall how to graph points in all four quadrants of the coordinate plane.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.8.12 Solve two-step linear equations where coefficients are less than 10 and answers are integers.
Mathematics
MA2019 (2019)
Grade: 8
Accelerated
9. Solve systems of two linear equations in two variables by graphing and substitution.

a. Explain that the solution(s) of systems of two linear equations in two variables corresponds to points of intersection on their graphs because points of intersection satisfy both equations simultaneously.

b. Interpret and justify the results of systems of two linear equations in two variables (one solution, no solution, or infinitely many solutions) when applied to real-world and mathematical problems. [Grade 8, 12]
Unpacked Content
Evidence Of Student Attainment:
Students:
  • graph a system of two linear equations, recognizing that the ordered pair for the point of intersection is the x-value that will generate the given y-value for both equations.
  • Recognize that graphed lines with one point of intersection (different slopes) will have one solution, parallel lines (same slope, different y-intercepts) have no solutions, and lines that are the same (same slope, same y-intercept) will have infinitely many solutions.
  • Use substitution to solve a system, given two linear equations in slope-intercept form or one equation in standard form and one in slope-intercept form.
  • Make sense of their solutions by making connections between algebraic and graphical solutions and the context of the system of linear equations.
Teacher 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.
Diverse Learning Needs:
Tags: equation, graphs, solution, system, system of equations
License Type: Custom Permission Type
See Terms: https://aptv.pbslearningmedia.org/help/terms-of-use/
For full descriptions of license types and a guide to usage, visit :
https://creativecommons.org/licenses
AccessibilityVideo resources: includes closed captioning or subtitles
Comments

Additional activity and practice pages are provided for this video lesson.

  This resource provided by:  
Author: Kristy Lacks
This site may contain links to other websites or content belonging to or originating from third parties or links to websites and features in banners or other advertising. Such external links are not investigated, monitored, or checked for accuracy, adequacy, validity, reliability, availability, or completeness by us. WE DO NOT WARRANT, ENDORSE, GUARANTEE, OR ASSUME RESPONSIBILITY FOR THE ACCURACY OR RELIABILITY OF ANY INFORMATION OFFERED BY THIRD-PARTY WEBSITES LINKED THROUGH THIS SITE.
Copyright © 2017, Alabama Learning Exchange
Alabama State Department of Education
Alabama State Department of Education