If the System Has Infinitely Many Solutions, Write the Solution

question 390

Multiple Choice

If the system has infinitely many solutions, write the solution set with x arbitrary.
- $$\begin{array} { l } \frac { 3 } { x } + \frac { 8 } { y } + \frac { 1 } { z } = - \frac { 2 } { 3 } \\\frac { 8 } { x } + \frac { 1 } { y } - \frac { 8 } { z } = \frac { 61 } { 24 } \\\frac { 1 } { x } + \frac { 1 } { y } + \frac { 4 } { z } = - \frac { 5 } { 8 }\end{array}$$

• A) \(\{ ( 6 , - 8 , - 6 ) \}\)
• B) \(\left\{ \left\{ \frac { 1 } { 6 } , - \frac { 1 } { 8 } , - \frac { 1 } { 6 } \right) \right\}\)
• C) \(\left\{ \left\{ \left( \frac { 1 } { 6 } , - \frac { 1 } { 8 } , \frac { 1 } { 6 } \right) \right\} \right.\)
• D) \(\{ ( 6 , - 8,6 ) \}\)

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Definitions:

Isopropyl Bromide

A brominated hydrocarbon with the chemical formula C3H7Br, used in organic synthesis as an alkylating agent.

Neopentyl Bromide

A primary alkyl halide with the formula CH3C(Br)(CH3)3, known for its resistance to nucleophilic substitution reactions.

Cyclohexanone

A six-membered cyclic ketone, important as an intermediate in the synthesis of nylon and other polymers.

α-Halogenation

A chemical process where a hydrogen atom in an organic molecule is replaced by a halogen atom through substitution.