How are Systems of Equations related to Equations and Functions?

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Objective

Students will understand how a linear equation can be represented as a system of equations graphically. They will be able to write an equation as a system and solve it both algebraically and graphically showing that both solutions are the same.

Big Idea

Every equation is really a system of equations! Students don't usually see it that way but this lesson will help them to make that connection. Students will practice writing simple linear equations as a system of two functions and finding the solution bo

Lesson Author

James Bialasik

Amherst, NY

Grade Level

Ninth grade

Subjects

Math

Algebra

Standards

HSA-REI.C.6

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

HSA-REI.D.11

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.*

MP2

Reason abstractly and quantitatively.

MP7

Look for and make use of structure.

MP8

Look for and express regularity in repeated reasoning.

Opening

15 minutes

Investigation

15 minutes

Investigation-Reflection

equations_functions_stu_work.jpg

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In questions #1-3, students will make connections with solving a system of equations algebraically and solving the system graphically. This serves as an introduction to the substitution method of solving a system of equations. Students are able to connect a procedure that they have mastered in 7th and 8th grade to the concept of functions. Students can also verify that the procedure extends to other functions such as absolute value and exponential functions. Solving abosolute value and exponential functions algebraically is not required but can be used as an extension.

Closure

15 minutes

Writing prompt: If someone from our class was absent today, how would you explain the lesson? What things did you find confusing that you might want to emphasize? What things were easy?

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