Curriculum / Math / 8th Grade / Unit 6: Systems of Linear Equations / Lesson 2
Math
Unit 6
8th Grade
Lesson 2 of 11
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Solve systems of linear equations by graphing.
The core standards covered in this lesson
8.EE.C.8.A — Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
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.B.6 — Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
8.F.B.4 — Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
This lesson draws on students’ abilities to graph linear equations in the coordinate plane (Unit 5). Students may need to review these skills alongside the lesson.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Graph the system of equations in the coordinate plane and identify the solution.
Graph the system of equations in the coordinate plane. Identify the solution to the system and verify it algebraically.
$${2x-3y=18}$$
$${2x+y=2}$$
Grade 8 Mathematics > Module 4 > Topic D > Lesson 25 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..
Line $$a$$ is shown on the coordinate grid. Construct line $$b$$ on the coordinate grid so that
Item MAT.08.TE.2.000EE.B.149 from Smarter Balanced Assessments' Sample Items is made available by Smarter Balanced Assessment Consortium. © The Regents of the University of California – Smarter Balanced Assessment Consortium. Accessed March 20, 2018, 12:38 p.m..
A set of suggested resources or problem types that teachers can turn into a problem set
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A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Graph the system of equations in the coordinate plane. Verify algebraically that your answer is the solution to the system.
$${2x-4y=8}$$
$${y={3\over2}x}$$
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 1
Lesson 3
Topic A: Analyze & Solve Systems of Equations Graphically
Define a system of linear equations and its solution.
8.EE.C.8.A
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) 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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