Reflection: Connection to Prior Knowledge What is the "Point" of Solving a System? - Section 2: Investigation


This investigation served the purpose of letting students discover what the solution to a system of equations really represents.  Namely, the point(s) that satisfies both equations at the same time.  You can see from the student work that students were able to substitute the solution point into both equations to show that each resulted in a true equation.  In the third example of student work, the student noticed correctly that there were no points that would make both of those equations true at the same time (parallel lines).  However, that same student made an arithmetic error when answering the final question.  They graphed the lines (both are representative of the same linear function) correctly.  But, their arithmetic mistake made it difficult for them to see that the point they chose did, in fact, satisfy both equations.  Because of this, they did not try to substitute a second coordinate.

  Connection to Prior Knowledge: Investigation Reflection
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What is the "Point" of Solving a System?

Unit 3: Systems of Equations
Lesson 3 of 13

Objective: Students will be able to connect to the meaning of solving a system of equations. Namely, that a line is made up from an infinite number of points that make that line's equation true. If we find a point that is on both lines that it has to make both equations true. Also that the other points on the line do not make both equations true.

Big Idea: This lesson is all about making connections between the solution to a system that students see graphically and what that solution means in terms of each equation. Students will have an opportunity to practice graphing systems of equations and showing what

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Math, graphing linear functions, Algebra, systems of equations, 9th grade
  45 minutes
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