A-REI.3.6

Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

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Formative Assessments
Formative Assessments
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Students are asked to solve a system of equations both algebraically and graphically.
Solving a System of Equations – 1
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Students are asked to solve a system of equations both algebraically and graphically.
Solving a System of Equations – 2
Assessment Logo. Includes a gray clipboard on a blue background.
Students are asked to solve a system of equations both algebraically and graphically.
Solving a System of Equations – 3
Virtual/Hands-on Manipulatives
Virtual/Hands-on Manipulatives
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Assessment Questions
Assessment Questions
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Videos of Expert Instruction
Videos of Expert Instruction
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The points of intersection of two graphs represent common solutions to both equations. Finding these intersection points is an important tool in analyzing physical and mathematical systems.
Systems of Linear Equations in Two Variables
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Hook/Performance Tasks
Hook/Performance Tasks
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The given solutions for this task involve the creation and solving of a system of two equations and two unknowns, with the caveat that the context of the problem implies that we are interested only in non-negative integer solutions. Indeed, in the first solution, we must also restrict our attention to the case that one of the variables is further even. This aspect of the task is illustrative of mathematical practice standard MP4 (Model with mathematics), and crucial as the system has an integer solution for both situations, that is, whether or not we include the dollar on the floor in the cash box or not.
Cash Box
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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.
Selling Fuel Oil at a Loss
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This task has some aspects of a mathematical modeling problem (SMP 4) and it also illustrates SMP 1 (Making sense of a problem). Students are given all the relevant information on the nutritional labels, but they have to figure out how to use this information. They have to come up with the idea that they can set up two equations in two unknowns to solve the problem.
Quinoa Pasta 2