In this lesson, students continue to develop their understanding of solving systems by elimination. Students are given a system that represents the quantities and constraints in a situation. They interpret, in context, the solutions to the individual equations and to the system. They then use the context to make sense of the sum of the two equations and why it shares a solution with the equations in the given system. Along the way, students begin to formulate a logical explanation as to why adding (or subtracting) the two equations in a system can be helpful for identifying the solution to the system (MP3).
Students also practice solving systems by adding and subtracting equations and checking their solutions. They also encounter systems where one variable cannot be easily eliminated (given what they know at this point), motivating the need for another strategy.
Lesson overview
 15.1 Warmup: Is It Still True? (5 minutes)
 15.2 Activity: Classroom Supplies (20 minutes)

15.3 Activity: A Bunch of Systems (10 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 15.4 Cooldown: Putting New Equations to Work (5 minutes)
Learning goals:
 Explain (orally and in writing) why adding or subtracting two equations that share a solution results in a new equation that also shares the same solution.
 Practice solving systems of linear equations by adding or subtracting equations to eliminate a variable.
 Use a context to make sense of an equation that is the sum of two equations in a system, and to reason about why this equation shares a solution with the system.
Learning goals (student facing):
 Let’s think about why adding and subtracting equations works for solving systems of linear equations.
Learning targets (student facing):
 I can explain why adding or subtracting two equations that share a solution results in a new equation that also shares the same solution.
Required materials:
 Graphing technology
Required preparation:
 Acquire devices that can run Desmos (recommended) or other graphing technology.
 It is ideal if each student has their own device. (Desmos is available under Math Tools.)
Standards:
 This lesson builds on the standard: CCSS.HSAREI.C.6MS.AREI.6MO.A1.REI.B.3
 This lesson builds towards the standard: CCSS.HSAREI.C.5MS.AREI.5MO.A1.REI.B.5
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