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