Curriculum / Math / 9th Grade / Unit 4: Linear Equations, Inequalities and Systems / Lesson 14
Math
Unit 4
9th Grade
Lesson 14 of 14
Jump To
Identify solutions to systems of equations with 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
Suggestions for teachers to help them teach this lesson
Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
What do you notice about the following system of equations?
$${2x+y-z=2}$$
$${-x-3y+z=-1}$$
$${-4x+3y+z=-4}$$
Below is a word problem and the system of equations that models the context. But, the definition of the variables is missing. Define the variables, solve the system, and give the solution in context of the problem.
A landlord owns three condominiums: a 1 bedroom condo, a 2-bedroom condo, and a 3-bedroom condo. The total rent she receives is $1,240. She needs to make repairs on the condos, and its costs 10% of the 1-bedroom condo’s rent for its repairs, 20% of the 2-bedroom condo’s rent for its repairs, and 30% of the 3-bedroom condo’s rent for its repairs. The total repair bill was $276. The 3-bedroom condo’s rent is twice the 1-bedroom condo’s rent. How much is the rent for each condo?
System:
$${x+y+z=1240}$$
$${.1x+.2y+.3z=276}$$
$${z=2x}$$
Word Problems in 3 Variables by Diane Ford is made available on Summer 2014 Math 80 Intermediate Algebra Course. Accessed Oct. 31, 2017, 1:11 p.m..
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.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Solve the system of equations:Â
$${x+3y+z=10}$$
$${x+y+z=2}$$
$${y-2z=2}$$
Algebra II Practice A.REI.C.6: Solving Linear Systems 4 is made available on JMAP by Steve Sibol and Steve Watson. Copyright © 2017 JMAP, Inc. - All rights reserved. Accessed Oct. 19, 2017, 4:30 p.m..
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 13
Topic A: Properties and Solutions of Two-Variable Linear Equations and Inverse Functions
Identify the solutions and features of a linear equation and when two linear equations have the same solutions.
A.REI.D.10 A.SSE.B.3
Write linear equations given features, points, or graph in standard form, point-slope form, and slope-intercept form.
A.SSE.B.3 F.IF.B.4 F.IF.C.7.A
Determine if a function is linear based on the rate of change of points in the function presented graphically and in a table of values.
F.IF.B.6 F.IF.C.7.A F.IF.C.9 F.LE.A.1.A
Identify inverse functions graphically and from a table of values in contextual and non-contextual situations.
F.BF.B.4.A F.IF.A.1 F.IF.A.2 F.IF.B.5
Find inverse functions algebraically, and model inverse functions from contextual situations.
A.CED.A.4 F.BF.B.4.A F.IF.B.6
Create a free account to access thousands of lesson plans.
Already have an account? Sign In
Topic B: Properties and Solutions of Two-Variable Linear Inequalities
Describe the solutions and features of a linear inequality. Graph linear inequalities.
A.REI.D.12
Write linear inequalities from graphs.
A.CED.A.3 A.REI.D.12
Write linear inequalities from contextual situations.
A.CED.A.3
Topic C: Systems of Equations and Inequalities
Solve a system of linear equations graphically.
A.CED.A.3 A.REI.D.11
Identify solutions to systems of inequalities graphically. Write systems of inequalities from graphs and word problems.
Solve linear systems of equations of two variables by substitution.
A.CED.A.3 A.REI.C.5 A.REI.C.6 N.Q.A.2
Identify solutions to systems of equations algebraically using elimination. Write systems of equations.
A.REI.C.5
Identify solutions to systems of equations using any method. Write systems of equations.
A.REI.A.1 A.REI.C.6 A.SSE.B.3
A.REI.C.6
See all of the features of Fishtank in action and begin the conversation about adoption.
Learn more about Fishtank Learning School Adoption.
Yes
No
Access rigorous, relevant, and adaptable math lesson plans for free