MA.912.AR.9.3

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Given a mathematical or real-world context, solve a system consisting of two-variable linear or non-linear equations algebraically or graphically.

Clarifications

Clarification 1: Within the Algebra 2 course, non-linear equations are limited to quadratic equations.
General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 912
Strand: Algebraic Reasoning
Standard: Write and solve a system of two- and three-variable equations and inequalities that describe quantities or relationships.
Date Adopted or Revised: 08/20
Status: State Board Approved

Related Courses

This benchmark is part of these courses.
1200330: Algebra 2 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200340: Algebra 2 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1202340: Precalculus Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7912095: Access Algebra 2 (Specifically in versions: 2016 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))
1209315: Mathematics for ACT and SAT (Specifically in versions: 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.912.AR.9.AP.3: Solve a system consisting of two-variable linear or quadratic equations algebraically or graphically.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Lesson Plans

Changes are Coming to System of Equations:

Use as a follow up lesson to solving systems of equations graphically. Students will explore graphs of systems to see how manipulating the equations affects the solutions (if at all).

Type: Lesson Plan

Space Equations:

In this lesson, students model the orbit of a satellite and the trajectory of a missile with a system of equations. They solve the equations both graphically and algebraically.

Type: Lesson Plan

Perspectives Video: Expert

Assessment of Past and Present Rates of Sea Level Change:

In this video, Brad Rosenheim describes how Louisiana sediment cores are used to estimate sea level changes over the last 10,000 years. Video funded by NSF grant #: OCE-1502753.

Type: Perspectives Video: Expert

Perspectives Video: Professional/Enthusiast

Solving Systems of Equations, Oceans & Climate:

Angela Dial discusses how she solves systems of equations to determine how the composition of ocean floor sediment has changed over 65 million years to help reveal more information regarding climate change.

Type: Perspectives Video: Professional/Enthusiast

Problem-Solving Tasks

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

Introduction to Linear Functions:

This task lets students explore the differences between linear and non-linear functions. By contrasting the two, it reinforces properties of linear functions.

Type: Problem-Solving Task

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Problem-Solving Tasks

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

Introduction to Linear Functions:

This task lets students explore the differences between linear and non-linear functions. By contrasting the two, it reinforces properties of linear functions.

Type: Problem-Solving Task

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

Problem-Solving Tasks

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

Introduction to Linear Functions:

This task lets students explore the differences between linear and non-linear functions. By contrasting the two, it reinforces properties of linear functions.

Type: Problem-Solving Task