Solve the System by Using Either the Substitution Method or the Elimination-By-Addition

question 224

Short Answer

Solve the system by using either the substitution method or the elimination-by-addition method, whichever seems more appropriate. $$\left( \begin{array} { r l l } \frac { 1 } { 2 } x &-& \frac { 1 } { 6 } y &= & - 1 \\\frac { 1 } { 2 } x &+ &\frac { 1 } { 4 } y &= & - 11\end{array} \right)$$ If the equations of the system are dependent, or if a system is inconsistent, so indicate. In those cases enter dependent or inconsistent . Otherwise, enter your answer as an ordered pair ( x , y ).

---

Definitions:

Total Revenue

The total amount of money a firm receives from the sale of its products or services, calculated by multiplying the price per unit by the number of units sold.

Economic Profits

Profits exceeding the total costs, including both explicit costs and implicit costs such as opportunity costs.

ATC

ATC, or average total cost, is the sum of all production costs divided by the quantity of output produced, encompassing both fixed and variable costs.

MC

Stands for Marginal Cost, which is the change in total cost that arises when the quantity produced is incremented by one unit; it is a key concept in economic theory guiding decision-making on the optimal level of production.