Curriculum / Math / 9th Grade / Unit 4: Linear Equations, Inequalities and Systems / Lesson 11
Math
Unit 4
9th Grade
Lesson 11 of 14
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Solve linear systems of equations of two variables by substitution.
The core standards covered in this lesson
A.CED.A.3 — Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
N.Q.A.2 — Define appropriate quantities for the purpose of descriptive modeling.
A.REI.C.5 — Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
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
Two trains leave different cities heading toward each other at different speeds. When and where do they meet?
Train A, traveling 70 miles per hour (mph), leaves Westford heading toward Eastford, 260 miles away. At the same time, Train B, traveling 60 mph, leaves Eastford heading toward Westford. When do the two trains meet? How far from each city do they meet?
Two Trains... by Jon Orr is made available on Mr. Orr is a Geek.com under the CC BY 4.0 license. Accessed Oct. 19, 2017, 4:08 p.m..
$${6x+3y=27}$$, find $$x$$ when $$y=x+4$$.
What is the value of $$y$$?
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
A child has a handful of coins of only dimes and nickels. The total amount of money is $1.10, and there is a total of 14 coins.
Write and solve a system of equations (using substitution). Identify the number of nickels and dimes that the child is holding.Â
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 10
Lesson 12
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
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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.
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
Identify solutions to systems of equations with three variables.
A.REI.C.6
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