Use Cramerʹs Rule to Solve the System of Equations $$\begin{array} { l } 2 x + 4 y + 8 z = 40 \\x + 2 y + 4 z = - 10 \\x + y + z = - 4\end{array}$$

question 131

Multiple Choice

Use Cramerʹs rule to solve the system of equations. If D = 0, use another method to determine the solution set.
- $$\begin{array} { l } 2 x + 4 y + 8 z = 40 \\x + 2 y + 4 z = - 10 \\x + y + z = - 4\end{array}$$

• A) Cramer's rule does not apply since \(D = 0\); \(\varnothing\)
• B) Cramer's rule does not apply since \(D = 0 ; \{ ( 2 z - 1 , z + 2 , z ) \}\)
• C) \(\{ ( - 5,3 , - 4 ) \}\)
• D) \(\{ ( - 4 , - 5,3 ) \}\)

---

Definitions:

Fixed Expenses

Costs that do not vary with the volume of production or sales, such as rent, salaries, and insurance premiums.

Contribution Margin Ratio

The proportion of sales revenue that exceeds variable costs, indicating how much revenue contributes to fixed costs and profit.

Margin of Safety Percentage

A financial ratio indicating the difference between actual sales and break-even sales, used to determine the risk of incurring a loss.

Break-even Sales

The level of sales at which a business neither makes a profit nor a loss, calculated by dividing fixed costs by the contribution margin ratio.