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13. Given: a-b-c-d, b=d-1, c = 6; Prove: a = 5 Statements Reasons

13. Given: a-b-c-d, b=d-1, c = 6; Prove: a = 5 Statements Reasons

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**13. Given:** \[ a - b = c - d, \quad b = d - 1, \quad c = 6; \quad \text{Prove:}\, a = 5 \] **Statements** | **Reasons** -----------------------------|----------------------- ____________________________ | ______________________ ____________________________ | ______________________ ____________________________ | ______________________ ____________________________ | ______________________ ____________________________ | ______________________ **14. Given:** \[ 5x + 4y = 24, \quad x + 7y = 11; \quad \text{Prove:}\, y = 1 \] **Statements** | **Reasons** -----------------------------|----------------------- ____________________________ | ______________________ ____________________________ | ______________________ ____________________________ | ______________________ ____________________________ | ______________________ ____________________________ | ______________________ **Explanation:** This image shows a problem-solving exercise that guides the student to prove the value of variable \( a \) given certain algebraic conditions. The statements and reasons columns are provided for a step-by-step logical progression to solve the given problem. In the first problem: - You are given the relationships between the variables \( a, b, c, \) and \( d \). - The goal is to use these relationships to prove that \( a \) equals 5. In the second problem: - You are given a system of linear equations involving \( x \) and \( y \). - The objective is to prove that \( y = 1 \) using these equations. Students will fill in the steps (statements) and justify them (reasons) to derive the required proofs. These types of exercises are commonly used to practice analytical thinking and problem-solving skills in mathematics, particularly in algebra.
Transcribed Image Text:**13. Given:** \[ a - b = c - d, \quad b = d - 1, \quad c = 6; \quad \text{Prove:}\, a = 5 \] **Statements** | **Reasons** -----------------------------|----------------------- ____________________________ | ______________________ ____________________________ | ______________________ ____________________________ | ______________________ ____________________________ | ______________________ ____________________________ | ______________________ **14. Given:** \[ 5x + 4y = 24, \quad x + 7y = 11; \quad \text{Prove:}\, y = 1 \] **Statements** | **Reasons** -----------------------------|----------------------- ____________________________ | ______________________ ____________________________ | ______________________ ____________________________ | ______________________ ____________________________ | ______________________ ____________________________ | ______________________ **Explanation:** This image shows a problem-solving exercise that guides the student to prove the value of variable \( a \) given certain algebraic conditions. The statements and reasons columns are provided for a step-by-step logical progression to solve the given problem. In the first problem: - You are given the relationships between the variables \( a, b, c, \) and \( d \). - The goal is to use these relationships to prove that \( a \) equals 5. In the second problem: - You are given a system of linear equations involving \( x \) and \( y \). - The objective is to prove that \( y = 1 \) using these equations. Students will fill in the steps (statements) and justify them (reasons) to derive the required proofs. These types of exercises are commonly used to practice analytical thinking and problem-solving skills in mathematics, particularly in algebra.
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