If the System Has Infinitely Many Solutions, Write the Solution

question 104

Multiple Choice

If the system has infinitely many solutions, write the solution set with x arbitrary.
- $$\begin{array} { l } \frac { 1 } { x } + \frac { 1 } { y } + \frac { 1 } { z } = - 1 \\\frac { 1 } { x } - \frac { 1 } { y } + \frac { 6 } { z } = - \frac { 10 } { 3 } \\\frac { 1 } { x } + \frac { 1 } { y } + \frac { 1 } { z } = - 1\end{array}$$

• A) \(\{ ( - 1,3,3 ) \}\)
• B) \(\left\{ \left\{ - 1 , \frac { 1 } { 3 } , - \frac { 1 } { 3 } \right) \right\}\)
• C) \(\{ ( 1 , - 3 , - 3 ) \}\)
• D) \(\{ ( - 1,3 , - 3 ) \}\)

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Definitions:

Median

The middle value in a sorted, ascending or descending, list of numbers.

Percentile

A value on a scale of 100 that indicates the percent of a distribution that is equal to or below it.

Quartiles

Divisions of a data set that mark three points to divide the data into four equal parts, each representing a quarter of the dataset.

Histogram

A graphical representation of data using bars of different heights to show the frequency of data in different intervals.