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Describe and correct the error in the first step of solving the system of linear equations. 5x + 3y = = 15 -x + 2y + 3 = 10 3.x - 4y + 32 = 8 X 5x + 3y = 15 -5.x+10y + 15z 10 13y + 14 = 25

Describe and correct the error in the first step of solving the system of linear equations. 5x + 3y = = 15 -x + 2y + 3 = 10 3.x - 4y + 32 = 8 X 5x + 3y = 15 -5.x+10y + 15z 10 13y + 14 = 25

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Title: Identifying and Correcting Errors in Solving Systems of Linear Equations** When solving systems of linear equations, accuracy in transformation and operation is crucial. Let's examine a set of equations and identify any mistakes in the initial solving steps. **System of Linear Equations:** 1. \( 5x + 3y - z = 15 \) 2. \( -x + 2y + 3z = 10 \) 3. \( 3x - 4y + 3z = 8 \) **Error Analysis in the Initial Step:** A boxed section in the image shows the equations being combined incorrectly: - **First Equation unchanged:** \( 5x + 3y - z = 15 \) - **Attempt to transform the second equation:** Incorrect transformation: \( -5x + 10y + 15z = 10 \) (This transformation suggests a multiplication by 5, but the constants need adjustment.) - **Incorrect resultant equation from these operations:** \( 13y + 14z = 25 \) **Explanation of the Error:** The second equation transformation introduces an error. When multiplying the entire equation by any number, each term, including the constants, must be adjusted, which did not happen correctly here. Verification of arithmetic and careful multiplication are needed to resolve such errors. **Correction Suggestion:** Carefully re-apply the operation steps, ensuring consistent multiplication across each element of an equation. Double-check results after calculations for precision before proceeding to the next steps.
Transcribed Image Text:**Title: Identifying and Correcting Errors in Solving Systems of Linear Equations** When solving systems of linear equations, accuracy in transformation and operation is crucial. Let's examine a set of equations and identify any mistakes in the initial solving steps. **System of Linear Equations:** 1. \( 5x + 3y - z = 15 \) 2. \( -x + 2y + 3z = 10 \) 3. \( 3x - 4y + 3z = 8 \) **Error Analysis in the Initial Step:** A boxed section in the image shows the equations being combined incorrectly: - **First Equation unchanged:** \( 5x + 3y - z = 15 \) - **Attempt to transform the second equation:** Incorrect transformation: \( -5x + 10y + 15z = 10 \) (This transformation suggests a multiplication by 5, but the constants need adjustment.) - **Incorrect resultant equation from these operations:** \( 13y + 14z = 25 \) **Explanation of the Error:** The second equation transformation introduces an error. When multiplying the entire equation by any number, each term, including the constants, must be adjusted, which did not happen correctly here. Verification of arithmetic and careful multiplication are needed to resolve such errors. **Correction Suggestion:** Carefully re-apply the operation steps, ensuring consistent multiplication across each element of an equation. Double-check results after calculations for precision before proceeding to the next steps.
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