Determine Whether the Two Systems of Linear Equations Yield the Same

question 37

Multiple Choice

Determine whether the two systems of linear equations yield the same solutions. If so, find the solutions using matrices. $\left\{ \begin{aligned}x - 8 y - 8 z & = - 36 \\y + 2 z & = 7 \\z & = 2\end{aligned} \right.$ $\left\{ \begin{aligned}x - 7 y + 5 z & = - 7 \\y + 2 z & = 7 \\z & = 2\end{aligned} \right.$

• A)x = 4, y = 3, z = 2
• B)x = -4, y = -3, z = 2
• C)x = -3, y = 2, z = 4
• D)x = 3, y = 2, z = 4
• E)The systems yield different solutions.

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Definitions:

Long-Run Equilibrium

A market state where all producers and consumers have fully adjusted to all changes, and there are no forces causing further adjustments.

Production Costs

The total expense incurred in manufacturing a product or providing a service, including raw materials, labor, and overheads.

Marginal Revenue

The increase in revenue achieved by selling one additional unit of a product or service.

Economic Profits

Profits calculated by subtracting both explicit and implicit costs from total revenues, often representing the additional benefit over the next best alternative.