# Linear Equations, Inequalities and Systems

## Objective

Solve linear systems of equations of two variables by substitution.

## Common Core Standards

### Core Standards

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• 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.

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• 8.EE.C.8

## Criteria for Success

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1. Identify the variables, relationship between the variables, and number of functions in system of equations problems.
2. Describe why solving by substitution works algebraically.
3. Describe the meaning of a solution to a system of linear equations in the context of a problem.
4. Describe any domain restrictions that are presented when a system is presented in a contextual situation.
5. Describe the equivalence of a solution found graphically and a solution found algebraically.

## Anchor Problems

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### Problem 1

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?

#### References

Mr. Orr Is a Geek.com Two Trains...

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..

Modified by The Match Foundation, Inc.

### Problem 2

${6x+3y=27}$, find $x$ when $y=x+4$

What is the value of $y$

## Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.