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
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
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.
Lesson 7
Lesson 9
Topic A: Features of Linear Functions
Identify features of linear functions from equations, verbal descriptions, tables, and graphs.
A.SSE.A.1.A F.IF.B.4 F.IF.C.9
Write linear functions that represent contextual situations.
F.IF.A.2 F.IF.B.4 F.IF.B.5
Solve for a desired quantity in a linear function.
A.CED.A.1 A.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.A F.BF.B.4.C
Find the inverse of contextual and non-contextual situations algebraically.
F.BF.B.4.A F.BF.B.4.B F.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.2 A.REI.C.6 F.IF.B.5
Describe the number of solutions of a system of equations. Verify algebraically.
A.REI.C.6 A.REI.D.11
A.REI.C.6
Identify the solution to a system of an absolute value equation and a linear function algebraically and graphically.
A.REI.D.11
Graph and identify solutions to systems of linear inequalities.
A.CED.A.3 A.REI.D.12 F.IF.B.5
Write systems of linear inequalities from a contextual situation.
A.CED.A.3 A.REI.D.12
Topic C: Piecewise Functions
Write and evaluate piecewise functions from graphs. Graph piecewise functions from algebraic representations.
A.CED.A.2 F.IF.C.7.B
Write piecewise functions from contextual situations.
A.CED.A.2 A.CED.A.3 F.IF.B.4 F.IF.C.7.B
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