If the System Has Infinitely Many Solutions, Write the Solution

question 369

Multiple Choice

If the system has infinitely many solutions, write the solution set with x arbitrary.
- $$\begin{array} { l } \frac { 2 } { x } - \frac { 1 } { y } - \frac { 2 } { z } = - \frac { 53 } { 20 } \\- \frac { 1 } { x } + \frac { 3 } { y } + \frac { 7 } { z } = \frac { 63 } { 20 } \\\frac { 3 } { x } - \frac { 1 } { y } - \frac { 1 } { z } = - \frac { 69 } { 20 }\end{array}$$

• A) \(\left\{ \left( - 1 , \frac { 1 } { 4 } , - \frac { 1 } { 5 } \right) \right\}\)
• B) \(\{ ( - 1,4 , - 5 ) \}\)
• C) \(\{ ( - 1,4,5 ) \}\)
• D) \(\left\{ \left( - 1 , \frac { 1 } { 4 } , \frac { 1 } { 5 } \right) \right\}\)

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Definitions:

Sample Size

Sample size refers to the number of observations or data points collected in a study.

Sampling Distribution

The arrangement of probabilities for a specified statistic, coming from a randomly chosen sample.

Sample Proportion

The fraction of the total sample that represents a particular trait or characteristic.

Normal Distribution

A probability distribution that is symmetric around the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.