Use Cramer's Rule to Solve the System of Equations $$\begin{aligned}x - y & + 5 z = 5 \\3 x & + z = 0 \\x + 4 y & + z = - 20\end{aligned}$$

question 207

Multiple Choice

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set.
- $$\begin{aligned}x - y & + 5 z = 5 \\3 x & + z = 0 \\x + 4 y & + z = - 20\end{aligned}$$

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

---

Definitions:

Variable Input

A factor of production, such as labor or raw materials, whose quantity can be changed easily by a business to adjust to the level of output.

Short Run

Short Run is a time period in economics during which at least one input is fixed while others are variable.

Fixed Input

A factor of production that cannot be easily increased or decreased in the short term, such as land or machinery.

Short Run

A period in which at least one input in the production process is fixed, limiting the ability of the firm to adjust production levels.