Curriculum / Math / 8th Grade / Unit 6: Systems of Linear Equations / Lesson 8
Math
Unit 6
8th Grade
Lesson 8 of 11
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Solve systems of linear equations using elimination (linear combinations) when there is already a zero pair.
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.
The foundational standards covered in this lesson
8.EE.C.7 — Solve linear equations in one variable.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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.Â
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
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.
$$x + 3 = 8Â $$
$$x - 4 = 1$$
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 US license. Accessed Dec. 2, 2016, 5:15 p.m..
Solve the system of equations below by using the elimination method. Write your answer as a coordinate point.
$${6x-5y=21}$$
$${2x+5y=-5}$$
Solve the three systems using the elimination method. Compare and contrast each solution.
$${{{4y+2x=12}}}$$
$${-4y-2x=12}$$
$${-4y-2x=-12}$$
$$-{{{4y+2x=12}}}$$
A set of suggested resources or problem types that teachers can turn into a problem set
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
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.
Solve the system.
$${9x+2y=9}$$ $${6x-2y=-4}$$
An example response to the Target Task at the level of detail expected of the students.
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.
Lesson 7
Lesson 9
Topic A: Analyze & Solve Systems of Equations Graphically
Define a system of linear equations and its solution.
8.EE.C.8.A
Solve systems of linear equations by graphing.
8.EE.C.8.A 8.EE.C.8.B
Classify systems of linear equations as having a unique solution, no solutions, or infinite solutions.
Solve real-world and mathematical problems by graphing systems of linear equations.
8.EE.C.8.C
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Topic B: Analyze & Solve Systems of Equations Algebraically
Solve systems of linear equations using substitution when one equation is already solved for a variable.
8.EE.C.8.B
Solve systems of linear equations using substitution by first solving an equation for a variable.
Solve real-world and mathematical problems using linear systems and substitution.
Solve systems of linear equations using elimination (linear combinations) by first creating a zero pair.
Solve real-world and mathematical problems using systems and any method of solution.
8.EE.C.8.B 8.EE.C.8.C
Model and solve real-world problems using systems of equations.
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