1.2C Lesson: Solving Linear Equations with Different Solving Outcomes* Name:
Period:
1. Two students, Arthur and Oliver, each have some chocolates. They know that they have the same number of chocolates. Arthur has two tubs of chocolates, three bags of chocolates, and twenty-five loose chocolates. Oliver has two tubs of chocolates, five and a half bags of chocolates, and fifteen loose chocolates. Can you determine how many chocolates are in a tub? How many chocolates are in a bag?
2.
Like Arthur and Oliver, Abby and Amy also say that they have the same number of chocolates. Abby has one full tub of chocolates and 21 loose chocolates. Amy has one full tub of chocolates and 17 loose chocolates. Each tub has the same number of chocolates. Can you determine how many chocolates are in a tub? Why or why not? If so, how many chocolates are in a tub?
3. Use the model to complete the following. a. What observations can you make?
b. Write the algebraic representation for this model and solve. Explain in words what happened when you solved the equation. What is it about the structure of the equation that led to the solution?
SDUHSD Math B Honors Module #1 - STUDENT EDITION 2016-2017
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c. Create a model that would result in the same solution as in part b. Write the algebraic representation for your model. Model
Algebraic Representation
4. Use the model to complete the following. a. What observations can you make?
b. Write the algebraic representation for this model and solve. Explain in words what happened when you solved the equation. What is it about the structure of the equation that led to the solution?
c. Create a model that would result in the same solution as in part b. Write the algebraic representation for your model. Model
SDUHSD Math B Honors Module #1 - STUDENT EDITION 2016-2017
Algebraic Representation
37
Directions: Without solving, determine the number of solutions by examining the structure of the equation. 5.
6.
7.
8.
Directions: Examine the structure of each equation. State if there are infinitely many solutions, no solution, or one solution. If there is one solution, solve the equation and state the solution. If there are infinitely many solutions or no solution, justify why using the structure of the equation. 9.
10.
11.
12.
13.
14.
15. Justify whether the equation one solution, state the solution.
has one solution, infinitely many solutions, or no solution. If it has
SDUHSD Math B Honors Module #1 - STUDENT EDITION 2016-2017
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16. Replace each ? in the equation below with a numerical or a variable expression so that the following conditions are satisfied. Justify your reasoning.
a. The solution set is 2
b. The solution set is infinitely many solutions
c. The solution set is no solution
17. What is it about the structure of an equation that leads to one solution, infinitely many solutions, or no solution? Complete the table below and provide examples to support your claim. One Solution
No Solution
Infinitely Many Solutions
Structure of Equation
Model
Algebraic Example
SDUHSD Math B Honors Module #1 - STUDENT EDITION 2016-2017
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