Use Cramerʹs Rule to Solve the System of Equations $$\begin{array} { r } x + y + z = - 1 \\x - y + 3 z = 7 \\3 x + y + z = - 3\end{array}$$

question 437

Multiple Choice

Use Cramerʹs rule to solve the system of equations. If D = 0, use another method to determine the solution set.
- $$\begin{array} { r } x + y + z = - 1 \\x - y + 3 z = 7 \\3 x + y + z = - 3\end{array}$$

• A) \(\{ ( 2 , - 2 , - 1 ) \}\)
• B) Cramer's rule does not apply since \(\mathrm { D } = 0\); \(\varnothing\)
• C) \(\{ ( - 1 , - 2,2 ) \}\)
• D) \(\{ ( 2 , - 1 , - 2 ) \}\)

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Definitions:

Monopolistically Competitive

A market structure in which many companies sell products that are similar but not identical, allowing for competition based on quality, price, and marketing.

Profit-Maximizing Price

The price level at which a company can sell its product or service to achieve the highest possible profit, taking into account the cost of production and market demand.

Average Total Cost

The total cost of production divided by the number of units produced, often used to identify the most efficient scale of production.

Efficient Level

The optimal point of production or operation at which a firm, economy, or system can produce goods or services with the minimum waste of resources.