Solve Systems of Equations by Graphing
Present scenario of which cell phone plan would be the best.
Choose which of the following cell-phone plans would be best. Why?
2 Direct Instruction
Watch and take notes on the lesson video.
3 Guided-Collaborative Practice
In a small group, or dyad, work on Activity 1: "Exploring Solutions to Linear Systems Graphically." from Cooperative Learning and Algebra 1 by Becky Bride. (pages 293-295)
Students wil ask and answer the questions with the group. Come to consensus on a solution.
Ask and answer the questions with the group. Come to consensus on each inquiry.
4 Formative Assessment
Students answer two questions:
What is the solution to the system?
- Students are given a system which they will graph and then answer the quick-question with the ordered pair.
Is the given ordered pair a solution to the system?
- Students are given an ordered pair and a system to determine if the solution is appropriate.
- What is the solution to the system? Give your answer as an ordered pair.
- Is the given ordered pair a solution to the system?
5 Independent Practice
Students complete pages 296 and 297 (or a selection of the 8 questions) to determine if they have a solid understanding of graphing systems and determining if an ordered pair is a solution of a given system.
For #1-4 on the first side, determine the solution of each system by graphing. Give your answer as an ordered pair.
For #1-4 on the second side, determine if the ordered pair is a solution of the given system.
Students will take a moment to identify the three types of systems they have explored graphically: parallel- inconsistent; intersecting - consistent/independent; concurrent-consistent/dependent.
Students will also give a written description of how to solve solutions graphically and how to determine if an ordered pair is the solution to a given system.
Draw the three types of systems and identify each.
Explain how to solve a system graphically
Explain how to determine if an ordered pair is the solution to a given system.
Key Standards Supported
Reasoning With Equations And Inequalities
|HSA.REI: Represent And Solve Equations And Inequalities Graphically|
|HSA.REI.10||Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).|
|HSA.REI.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.★|
|HSA.REI.12||Graph the solutions to a linear inequality in two variables as a half- plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.|
|Solve Systems Of Equations|
|HSA.REI.5||Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.|
|HSA.REI.6||Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.|