Curriculum / Math / 8th Grade / Unit 6: Systems of Linear Equations / Lesson 6
Math
Unit 6
8th Grade
Lesson 6 of 11
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Solve systems of linear equations using substitution by first solving an equation for a variable.
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 second of three lessons on substitution. In Lesson 6, students solve an equation for a variable first before substituting, and look at examples with no or infinite solutions. In Lesson 7, students will apply this strategy of solving systems to real-world applications.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Solve the system of linear equations using substitution. Describe how you can solve any system using substitution.
$${x+2y=8}$$ $${-3x+2y=16}$$
Solve the two systems below using substitution. Compare and contrast the two solutions. What do they each mean?
$${y=2(-x+3)}$$
$${2x+y=4}$$
$${5x+20y=15}$$
$${x+4y=3}$$
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.
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Determine by inspection if each system below has a unique solution, no solution, or infinite solutions. If the system has a unique solution, use substitution to find the coordinate point where the two lines intersect.
$${y=-3x+5}$$
$${2y=-6x+10}$$
$${x+y=8}$$
$${2x+y=-6}$$
$${x+y=3}$$
$${2x+2y=3}$$
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 5
Lesson 7
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 real-world and mathematical problems using linear systems and substitution.
Solve systems of linear equations using elimination (linear combinations) when there is already a zero pair.
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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