Solve the System A) No Solution; Inconsistent
B) $\{ ( - 2 , - 6,1 ) \}$

question 23

Multiple Choice

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent.
- $$\begin{aligned}x - \frac { 3 } { 4 } y + \frac { 5 } { 4 } z & = \frac { 15 } { 4 } \\- \frac { 1 } { 4 } x + \frac { 1 } { 2 } y + \frac { 1 } { 8 } z & = - \frac { 19 } { 8 } \\- \frac { 5 } { 2 } x + \frac { 9 } { 2 } y + z & = - 21\end{aligned}$$

• A) No solution; inconsistent
• B) \(\{ ( - 2 , - 6,1 ) \}\)
• C) \(\{ ( 0,0,0 ) \}\)
• D) \(\{ ( 2,1,2 ) \}\)

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Definitions:

Theory

A systematic framework of concepts and purposes designed to explain specific phenomena or predict future outcomes based on empirical evidence.

Phenomenon

An observable event or fact, especially one that is not fully understood, distinguished by its remarkable or unusual nature.

Interrelated Hypotheses

Interrelated hypotheses are hypotheses that are connected or have a logical relationship with each other within a broader research context.

Parsimony

The principle that among competing hypotheses that predict equally well, the one with the fewest assumptions should be selected.