Curriculum / Math / 8th Grade / Unit 6: Systems of Linear Equations / Lesson 1
Math
Unit 6
8th Grade
Lesson 1 of 11
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Lesson Notes
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Define a system of linear equations and its solution.
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.
The foundational standards covered in this lesson
6.EE.B.5 — Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
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
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Consider the graph below, showing two lines: L1 and L2.
a. What is the equation for each line?
b. Find a point, other than the ones given in the graph, that is a solution to L1 but not L2.
c. Is the point (4, 21) a solution to L1? Is it a solution to L2? Justify your response using your equations from Part (a).
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Two Lines, accessed on March 10, 2017, 11:13 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
Estimate the solution to each system graphed below.
a.
b.
A system of linear equations and the corresponding graph are shown below.
$${y=2x-4}$$
$${y={-{2\over3}}x+4}$$
Identify the solution to the system and then prove the solution algebraically.
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15-20 minutes
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A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
A system of linear equations is represented in the graph below.
a. Write the two equations that represent this system.
b. What is the solution to the system? Prove this algebraically.
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.
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Solve systems of linear equations by graphing.
Topic A: Analyze & Solve Systems of Equations Graphically
Standards
8.EE.C.8.A
8.EE.C.8.A8.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.B8.EE.C.8.C
Model and solve real-world problems using systems of equations.
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