Generated on 6/7/2026 at 9:16 PM
The webpage this document was printed/exported from can be found at the following URL:
https://www.cpalms.org//PreviewStandard/Preview/5497

Domain-Subdomain #: MAFS.8.EE.3.8Archived Standard

Analyze and solve pairs of simultaneous linear equations.

  1. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
  2. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
  3. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

Domain-Subdomain Information

General Information

Subject Area: Mathematics
Grade: 8
Domain-Subdomain: Expressions & Equations
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations. (Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
Date Adopted or Revised: 02/14
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes

Formative Assessments

Lesson Plans

  • Battle on the High Seas: Applying Systems of Linear Equations This lesson is designed to introduce solving systems of linear equations in two variables by graphing. Students will find the solutions of systems of linear equations in two variables by graphing "paths" of battleships and paths of launched torpedoes targeting them. The solutions of the systems will represent the intersection of the paths of a targeted ship (modeled by a linear equation) and the path of a torpedo from a battleship (modeled by another linear equation).
  • Classifying Solutions to Systems of Equations This lesson is intended to help teachers assess how well students are able to classify solutions to a pair of linear equations by considering their graphical representations. In particular, this lesson aims to help teachers identify and assist students who have difficulties in using substitution to complete a table of values for a linear equation, identifying a linear equation from a given table of values, and/or graph, and solving linear equations.
  • A Scheme for Solving Systems Students will graph systems of linear equations in slope-intercept form to find the solution to the system. Students will practice with systems that have one solution, no solution, and all solutions. Because the lesson builds upon a group activity, the students have an easy flow into the lesson and the progression of the lesson is a smooth transition into solving systems algebraically.
  • Where does my string cross? Students will graph a system of linear equations using pieces of string that intersect and discover what the point of intersection has to do with both equations. It will get tricky when the strings do not intersect, or when they transform into the same line.
  • Put Your Money Where Your Mouth Is Students will learn to find the solutions to a system of linear equations, by graphing the equations.
  • Exploring Systems of Equations using Graphing Calculators This lesson plan introduces the concept of graphing a system of linear equations. Students will use graphing technology to explore the meaning of the solution of a linear system including solutions that correspond to intersecting lines, parallel lines, and coinciding lines.
    Students will also graph linear systems by hand.
  • Exploring Systems with Piggies, Pizzas and Phones This is an introductory lesson on solving systems of equations using substitution and elimination methods. First, images are used to represent the variables (two stars and one heart) in the “equations” for students to solve. This allows students to intuitively consider logical solution strategies. Next, a bridge to the more formal solution methods is built. Students examine the algebraic representations for these logical strategies by examining sample student work.
  • Human systems of linear equations Students will work in cooperative groups to demonstrate solving systems of linear equations. They will form lines as a group and see where the point of intersection is.
  • Solving Real-Life Problems: Baseball Jerseys This graphing equations and inequalities lesson is intended to help you assess how well students are able to: Interpret a situation and represent the variables mathematically, select appropriate mathematical comparison methods to use, explore the effects of systematically varying the constraints, interpret and evaluate the data generated and identify the break-even point, checking it for confirmation, and communicate their reasoning clearly.

Problem-Solving Tasks

  • Interpreting the Graph The purpose of this task is to help students learn to read information about a function from its graph, by asking them to show the part of the graph that exhibits a certain property of the function. The task could be used to further instruction on understanding functions or as an assessment tool, with the caveat that it requires some amount of creativity to decide how to best illustrate some of the statements.
  • Quinoa Pasta 1 This task asks students to find the amount of two ingredients in a pasta blend. The task provides all the information necessary to solve the problem by setting up two linear equations in two unknowns. This progression of tasks helps distinguish between 8th grade and high school expectations related to systems of linear equations.
  • Cell Phone Plans This task presents a real-world problem requiring the students to write linear equations to model different cell phone plans. Looking at the graphs of the lines in the context of the cell phone plans allows the students to connect the meaning of the intersection points of two lines with the simultaneous solution of two linear equations. The students are required to find the solution algebraically to complete the task.
  • Two Lines In this task, we are given the graph of two lines including the coordinates of the intersection point and the coordinates of the two vertical intercepts and are asked for the corresponding equations of the lines. It is a very straightforward task that connects graphs and equations and solutions and intersection points.
  • Selling Fuel Oil at a Loss The task is a modeling problem which ties in to financial decisions faced routinely by businesses, namely the balance between maintaining inventory and raising short-term capital for investment or re-investment in developing the business.
  • Kimi and Jordan Students are asked to create and graph linear equations to compare the savings of two individuals. The purpose of the table in (a) is to help students complete (b) by noticing regularity in the repeated reasoning required to complete the table.
  • Fixing the Furnace Students are asked to write equations to model the repair costs of three different companies and determine the conditions for which each company would be least expensive. This task can be used to both assess student understanding of systems of linear equations or to promote discussion and student thinking that would allow for a stronger solidification of these concepts. The solution can be determined in multiple ways, including either a graphical or algebraic approach.
  • How Many Solutions? The student is given the equation 5x-2y=3 and asked, if possible, to write a second linear equation creating systems resulting in one, two, infinite, and no solutions.

Tutorials

Collections

MFAS Formative Assessments

Printed On: 6/8/2026 1:16:21 AM
Print Page | Close this window