If Possible, Solve the System of Equations $$\begin{array} { l } \frac { 1 } { 4 } x + \frac { 1 } { 4 } y = 1 \\\frac { 1 } { 2 } x - \frac { 1 } { 2 } y = - 1\end{array}$$

question 13

Multiple Choice

If possible, solve the system of equations. Use any method. If there is not a unique solution to a system, say why.
- $$\begin{array} { l } \frac { 1 } { 4 } x + \frac { 1 } { 4 } y = 1 \\\frac { 1 } { 2 } x - \frac { 1 } { 2 } y = - 1\end{array}$$

• A) \((\)\quad )\)
• B) \((\),\quad )\)
• C) No solution; inconsistent system of equations
• D) \(( - 1,4 )\)

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Definitions:

Truth Table

A logical table used to determine the validity of a proposition by listing all possible scenarios and their outcomes.

Atomic Sentences

The most basic statements in logic that cannot be broken down into simpler components while retaining truth values.

Truth Values

Values indicating the relation of a statement to truth, typically "true" or "false."

Atomic Sentences

Simple sentences that contain no logical connectors and cannot be broken down into smaller components.