Linear Equations, Inequalities and Systems

Lesson 13

Objective

Identify solutions to systems of equations using any method. Write system of equations and inequalities.

Common Core Standards

Core Standards

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  • A.REI.A.1 — Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

  • 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.

  • A.SSE.B.3 — Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.

Foundational Standards

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  • 8.EE.C.8

Criteria for Success

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  1. Choose an efficient method to solve systems of equations or inequalities. 
  2. Identify substitution as an efficient strategy when one variable has a coefficient of 1. 
  3. Identify elimination as an efficient strategy when no variables have a coefficient of 1 and no equations are easily solvable for one variable. 
  4. Identify graphing as an efficient strategy when there is more analysis that needs to be done of the situation and a graph would be helpful with this. 
  5. Explain that, regardless of method, the solution to the system will be the same.

Anchor Problems

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Problem 1

Which strategy would you use to solve each of the following problems? Justify your answer. (You do not need to solve them.)

  1.      $${\left\{\begin{matrix}2x-6y=24 \\ x+4y=16 \end{matrix}\right.}$$

 

  1.      $${\left\{\begin{matrix}4x-3y=15 \\ 2x+9y=32 \end{matrix}\right.}$$

Guiding Questions

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Problem 2

Greg wants to buy a new car. He looks at two different models. Car A costs $40,000, and he estimates it will cost $2,000 per year for gas and maintenance. Car B costs $60,000, and he estimates it will cost about $1,000 per year for gas and maintenance. Under what circumstances would it make sense for Greg to buy Car A? Under what circumstances would it make sense for Greg to buy Car B? Justify your answer. 

Guiding Questions

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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.

Target Task

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The basketball team sold t-shirts for a fundraiser. They sold a total of 23 items and made a profit of $246. They made a profit of $10 for every t-shirt they sold and $12 for every hat they sold.

Determine the number of t-shirts and the number of hats the basketball team sold. 

References