Objective
Solve systems of linear equations using elimination (linear combinations) when there is already a zero pair.
Common Core Standards
Core Standards
The core standards covered in this lesson
8.EE.C.8.B— Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
Expressions and Equations
8.EE.C.8.B— Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
Foundational Standards
The foundational standards covered in this lesson
8.EE.C.7
Expressions and Equations
8.EE.C.7— Solve linear equations in one variable.
Criteria for Success
The essential concepts students need to demonstrate or understand to achieve the lesson objective
- Understand that adding equivalent expressions will maintain the equivalence; equations can be added together.
- Understand elimination as an algebraic approach to solving a system of equations.
- Define and identify zero pairs in systems of equations.
- Solve systems of equations using elimination.
Tips for Teachers
Suggestions for teachers to help them teach this lesson
This is the first of two lessons on solving systems using elimination or linear combinations. In Lesson 8, students focus on the concepts behind elimination and why it works. Students look at problems that already contain a zero pair and do not require multiplication. In Lesson 9, students will learn how to multiply one or both equations in order to use this method.
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Anchor Problems
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Problem 1
Investigate if you can add equations to each other and still maintain balance and equality.
a.Given:
$$2 + 5 = 7$$, and
$$1 + 9 = 10$$
Does$$(2 + 5) + (1 + 9) = 7 + 10$$?
Does$$(2+1) + (5+9) = 7 + 10$$?
b.Given
$$-3 + 11 = 8$$, and
$$7 - 2 = 5$$
Does$$ (-3 + 11) + (7 - 2) = 8 + 5$$?
Does$$(-3 + 7) + (11 - 2) = 8 + 5$$?
c.Based on your conclusion from parts (a) and (b), write a single equation that accounts for both equations below.
$$x + 3 = 8$$
$$x - 4 = 1$$
Guiding Questions
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References
EngageNY Mathematics Grade 8 Mathematics > Module 4 > Topic D > Lesson 28—Example 1
Grade 8 Mathematics > Module 4 > Topic D > Lesson 28 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 USlicense.Accessed Dec. 2, 2016, 5:15 p.m..
Modified by Fishtank Learning, Inc.
Problem 2
Solve the system of equations below by using the elimination method. Write your answer as a coordinate point.
$${6x-5y=21}$$
$${2x+5y=-5}$$
Guiding Questions
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Problem 3
Solve the three systems using the elimination method. Compare and contrast each solution.
| System A | System B | System C |
$${{{4y+2x=12}}}$$ $${-4y-2x=12}$$ | $${{{4y+2x=12}}}$$ $${-4y-2x=-12}$$ | $${{{4y+2x=12}}}$$ $$-{{{4y+2x=12}}}$$ |
Guiding Questions
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Problem Set
A set of suggested resources or problem types that teachers can turn into a problem set
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Target Task
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Problem 1
Tamar writes two equations:
$$2y=4x+14$$
$$-2y=-4x-14$$
Tamar says that together, the two equations create a system with no solution because both equations have the same slope.
Do you agree with Tamar? Explain your reasoning.
Problem 2
Solve the system.
$${9x+2y=9}$$
$${6x-2y=-4}$$
Student Response
An example response to the Target Task at the level of detail expected of the students.
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Additional Practice
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
- Include problems where students solve systems using elimination to reinforce the procedure and process; ensure problems all have a zero pair and do not yet require multiplication; include problems that are no solution or infinite solution.
- Kuta Software Free Algebra 1 Worksheets Solving Systems of Equations by Elimination—Only use #1–4, or change the equations in the other examples to include a zero pair.
Lesson 7
Lesson 9
