Determine Whether the System Is Consistent A) $\mathrm { Yes }$

question 28

Multiple Choice

Determine whether the system is consistent.
- $$\begin{aligned}5 x _ { 2 } + x _ { 4 } & = - 11 \\x _ { 1 } + x _ { 2 } + 6 x _ { 3 } - x _ { 4 } & = 15 \\5 x _ { 1 } + x _ { 3 } + 6 x _ { 4 } & = 16 \\x _ { 1 } + x _ { 2 } + 3 x _ { 3 } & = 8\end{aligned}$$

• A) \(\mathrm { Yes }\)
• B) \(\mathrm { No }\)

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Definitions:

Sound Argument

An argument that is both valid (correctly structured such that if the premises are true, the conclusion must be true) and has all true premises.

Valid

Logically sound, where the conclusion necessarily follows the premises without any logical fallacies.

Premises

Statements or propositions that are presupposed and provide support for a conclusion in an argument.

Inductive Argument

A form of reasoning where the conclusion is supported by the premises but is not guaranteed to be true.