Solve the System of Equations by the Substitution Method $\left\{ \begin{array} { l } x + 8 y = - 7 \\- 7 x + 7 y = - 77\end{array} \right.$

question 142

Multiple Choice

Solve the system of equations by the substitution method.
- $\left\{ \begin{array} { l } x + 8 y = - 7 \\- 7 x + 7 y = - 77\end{array} \right.$

• A) \(( - 9 , - 1 )\)
• B) \(( 8 , - 1 )\)
• C) no solution
• D) \(( 9 , - 2 )\)

---

Definitions:

Constrained Optimization

The process of finding the maximum or minimum value of a function subject to certain constraints, common in economics to find the optimal resource allocation.

Cobb-Douglas

A form of production function that represents the relationship between two or more inputs (typically labor and capital) and the amount of output produced, characterized by constant returns to scale and substitution between inputs.

Constrained Optimization

The process of finding the optimal solution or outcomes within given limitations or constraints.

Maximizing Utility

Refers to the economic principle where individuals or firms seek to get the highest level of satisfaction from their resources.