Choose the values for a and b that results into a equation with no solution. **Problem 7**Choose the values for $ a $ and $ b $ that result in an equation with no solution.Given the equation:\[ 7x + b = ax - 6 \]**Options:**- $ a = -6 $- $ a = 7 $- $ a = 1 $- $ a = -42 $- $ b = -6 $- $ b = 7 $- $ b = 1 $- $ b = -42 $**Explanation:**To have an equation with no solution, the equations must be parallel, meaning they have the same slope but different y-intercepts. Here, we look for values of $ a $ and $ b $ such that the equation $ 7x + b = ax - 6 $ has no solution. This happens when $ a = 7 $ (to match the coefficient of $ x $) but $ b $ is not equal to $-6$.

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Answered: 7x + b = ax - 6 a = -6 a = 7 a = 1

Math

Algebra

7x + b = ax - 6 a = -6 a = 7 a = 1

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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A: Solution of the problem as follows

Question

Choose the values for a and b that results into a equation with no solution.

**Problem 7**

Choose the values for $ a $ and $ b $ that result in an equation with no solution.

Given the equation:

\[ 7x + b = ax - 6 \]

**Options:**

- $ a = -6 $
- $ a = 7 $
- $ a = 1 $
- $ a = -42 $
- $ b = -6 $
- $ b = 7 $
- $ b = 1 $
- $ b = -42 $

**Explanation:**

To have an equation with no solution, the equations must be parallel, meaning they have the same slope but different y-intercepts. Here, we look for values of $ a $ and $ b $ such that the equation $ 7x + b = ax - 6 $ has no solution. This happens when $ a = 7 $ (to match the coefficient of $ x $) but $ b $ is not equal to $-6$.

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