Solve the System by the Method of Your Choice $$\begin{array} { l } y = 13 - 3 x \\12 x + 4 y = 52\end{array}$$

question 86

Multiple Choice

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets.
- $$\begin{array} { l } y = 13 - 3 x \\12 x + 4 y = 52\end{array}$$

• A) \(\{ ( 0,13 ) \}\)
• B) \(\{ ( 5 , - 2 ) \}\)
• C) \(\{ ( x , y ) \mid 3 x + y = 13 \}\)
• D) \(\varnothing\)

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Definitions:

Feasible Solution

A potential solution to a problem that meets all the given constraints and requirements.

Optimal Solution

The best possible outcome from a set of choices, often found through specific methodologies in decision-making processes.

Improvement Indices

Metrics or indicators used to measure and track the effectiveness of improvements or changes made within a system or process.

Northwest-Corner Rule

A method used in transportation problems of operations research to find an initial feasible solution by allocating supplies to demands starting from the northwesternmost position.