Curriculum / Math / 11th Grade / Unit 1: Linear Functions and Applications / Lesson 8
Math
Unit 1
11th Grade
Lesson 8 of 13
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Solve a system of three equations in three variables.
The core standards covered in this lesson
A.REI.C.6 — Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
The foundational standards covered in this lesson
8.EE.C.8 — Analyze and solve pairs of simultaneous linear equations.
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
Determine the values for $${x, y}$$, and $$z$$ in the following system:
$$2x + 3y - z =5$$
$$4x - y -z = -1$$
$$x + 4y + z = 12$$
Algebra II > Module 1 > Topic C > Lesson 30 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..
In a bicycle shop, there are different numbers of bicycles, tricycles, and tandem bikes. There are a total of 144 front-steering handlebars, 378 pedals, and 320 wheels.
Below is a chart of how many front-steering handlebars, pedals, and wheels each vehicle contains.
How many bicycles, tricycles, and tandem bikes are in the shop?
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
For the following system, determine the values of $${p, q,}$$ and $$r$$ that satisfy all three equations:
$$2p + q - r =8$$
$$q + r = 4$$
$${p- q =2}$$
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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Identify the solution to a system of an absolute value equation and a linear function algebraically and graphically.
Topic A: Features of Linear Functions
Identify features of linear functions from equations, verbal descriptions, tables, and graphs.
Standards
A.SSE.A.1.AF.IF.B.4F.IF.C.9
Write linear functions that represent contextual situations.
F.IF.A.2F.IF.B.4F.IF.B.5
Solve for a desired quantity in a linear function.
A.CED.A.1A.CED.A.4
Find the inverse of a contextual situation graphically and describe the meaning of the function and its inverse.
F.BF.B.4.AF.BF.B.4.C
Find the inverse of contextual and non-contextual situations algebraically.
F.BF.B.4.AF.BF.B.4.BF.BF.B.4.C
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Topic B: Systems of Functions and Constraints
Write a system of functions for contextual situations and solve algebraically. Describe the solutions in context of the problem.
A.CED.A.2A.REI.C.6F.IF.B.5
Describe the number of solutions of a system of equations. Verify algebraically.
A.REI.C.6A.REI.D.11
A.REI.C.6
A.REI.D.11
Graph and identify solutions to systems of linear inequalities.
A.CED.A.3A.REI.D.12F.IF.B.5
Write systems of linear inequalities from a contextual situation.
A.CED.A.3A.REI.D.12
Topic C: Piecewise Functions
Write and evaluate piecewise functions from graphs. Graph piecewise functions from algebraic representations.
A.CED.A.2F.IF.C.7.B
Write piecewise functions from contextual situations.
A.CED.A.2A.CED.A.3F.IF.B.4F.IF.C.7.B
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