Use the clicker to change the value of a. What is the equation in standard form of the plane shown on the page? Sample Answers: 2x + 10y – z = 0 b. This page shows a graph of a linear function, z = ax + by + d.
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Some students might suggest that it is still a line, others might be familiar with planes, and others might predict that it is a more complicated function in 2-space because of the added variable. What do you think the graph of such a function might look like? Why? Sample Answers: Student predictions will vary. A linear equation in three variables is an equation of the standard form ax + by + cz = d. Moreover, if two lines do not intersect, that indicates that the system has no solutions. The intersection point lies on the graph of both functions, and therefore the coordinates of the point satisfy the system. The intersection indicates a point that satisfies both equations simultaneously. Sample Answers: One looks for the intersection point of the lines to indicate the solution of the system.
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When solving a system of two linear equations with two variables, what do you look for graphically to indicate the solution? Explain. Use Quick Poll to assess students’ understanding.ġ. Use Screen Capture to examine patterns that emerge. Investigate the graphical representations of solutions of a ĭetermine the number of solutions a system of linear Lesson Files: Student Activity 3x3_Linear_Systems_of_Equati ons_Student.pdf 3x3_Linear_Systems_of_Equati ons_Student.doc TI-Nspire document 3x3_Linear_Systems_of_Equati ons.tns Plot systems of three linear functions in three variables to Plot systems of two linear functions in three variables to investigate the graphical representations of solutions of a system. Manipulate a plane to observe the effect of the coefficients on the graph of the plane. This lesson involves connecting graphical representations of systems of linear equations in three variables to the number of Tech Tips: Make sure the font size on your TI-Nspire handhelds is set to Medium.
3x3 linear equation systems activity download#
Download a TI-Nspire document Open a document Move between pages Grab and drag a point Students will look for and make use of structure (CCSS Mathematical Practice). Students will construct viable arguments and critique the reasoning of others (CCSS Mathematical Practice). Students will be able to describe the conditions under which a system of linear equations in three variables will have 0, 1, or TI-Nspire™ Technology Skills: Students will be able to identify the number of solutions to a system of linear equations in three variables by analyzing the graphs of the equations. Students will be able to describe the effects of the coefficients of a linear function in three variables on the graph of the function.