Lesson 2: 6-2 Substitution
Duration of Days: 3
Lesson Objective
Solve systems of equations by using substitution.
Solve real-world problems involving systems of equations by using substitution.
How can you check a solution of a system of equations?
If the result of solving by substitution is an identity, then how many solutions are there?
If the result of solving by substitution results in a false statement, then how many solutions are there?
substitution
A.CED.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.
A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
SAT questions related to systems: 4-3-16,1-3-18,1-3-9,2-3-2,8-3-18,6-4-11,7-3-3,1-3-11,7-4-11,1-4-19,8-3-10,2-4-29,2-3-20,3-3-9
The substitution method uses the Substitution Property of Equality to solve systems of equations. In the system y = x + 5 and x + y = -11, I can substitute x + 5 for y in the second equation to solve the system. Then I can substitute the result, x = -8 into either equation to find a value for y.
A nature center charges $35.25 for a yearly membership and $6.25 for a single admission. Last week it sold a combined total of 50 yearly memberships and single admissions for $660.50. How many memberships and how many single admissions were sold?
Point out that if neither of the equations gives one variable in terms of the other, you must solve for one variable first. The easiest choice in Example 2 is to solve the first equation for x by subtracting 2y from both sides.
In Exercise 27, remind students that both Guillermo and Cara could be wrong, and that errors can be made in interpreting a solution as well as finding it.
Beginning Ask questions about the lesson content to elicit yes/no answers: “Look at Example 1. Is one of the equations solved for one of the variables?” yes “Is the first step of solving the system complete?” yes
Intermediate/Advanced Ask questions about the lesson content to elicit short answers: “Look at Example 1. Which equation is solved for a variable?” the first “What should be substituted for y in the second equation?” 2x + 1
Advanced High Ask questions about lesson content to elicit complete sentences: “How does Example 1 compare to Example 2?” In Example 1, Step 1 is already completed. “How would you choose the variable to solve for to solve Example 2 by substitution?” Solving the first equation for x makes sense because its coefficient is 1.
Practice: Exercises 1 - 7
Exercises 32-39
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