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Solving Linear Equations with Substitution: Refrigerator Dilemma

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Solving Linear Equations with Substitution: Refrigerator Dilemma

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Questions and Answers

In solving linear equations with the substitution method, why is it important to simplify whenever possible?

To show proficiency in mathematical simplification

To ensure the accuracy of the final solution (correct)

To make the calculations easier and quicker

To eliminate any possibility of making a mistake

Why do we choose one of the unknowns to be the subject in one of the equations when using the substitution method?

To create a new equation

To make calculations simpler

To eliminate one unknown variable (correct)

To substitute values directly

What is the purpose of substituting the modified equation back into the original equations in the substitution method?

To complicate the calculations

To increase the complexity of the problem

To check if the solutions are consistent (correct)

To introduce more variables

When solving for x and y in 2x + 3y = 8 and 3x - 2y = -1, what is the first step after choosing x as the subject in the first equation?

Subtracting 3y from both sides Signup and view all the answers

Why is it necessary to solve for one unknown variable before determining the remaining unknown when using the substitution method?

To reduce computational errors Signup and view all the answers

What does y represent in the context of the refrigerator example?

Total cost of the refrigerator Signup and view all the answers

In solving the equation 12y - 610x = 19200 for refrigerator 1, what does x represent?

Number of years the refrigerator is used Signup and view all the answers

What is the relationship between x and y after 5 years for both refrigerators?

The total cost for both refrigerators will remain the same Signup and view all the answers

What happens to the total cost comparison between refrigerators after 5 years?

The more expensive unit becomes less expensive Signup and view all the answers

In the context of the equations for refrigerators 1 and 2, what does y = 1830 + 47x represent?

Total cost of refrigerator 2 Signup and view all the answers