A financial analyst models a company's weekly metrics using three variables—revenue $R$ , operating cost $C$ , and advertising expenditure $A$ , measured in thousands of dollars. The metrics satisfy the following system of linear equations, where $k$ is a real constant:
$\begin{aligned} 4R - 3C + 2A &= 18 \\ R + 5C - 6A &= 14 \\ 5R + 2C - 4A &= k \end{aligned}$
If this system of linear equations is consistent (has at least one solution), what is the value of $k$ ?

Question

A financial analyst models a company's weekly metrics using three variables—revenue

R

, operating cost

C

, and advertising expenditure

A

, measured in thousands of dollars. The metrics satisfy the following system of linear equations, where

k

is a real constant:

\begin{aligned} 4R - 3C + 2A &= 18 \\ R + 5C - 6A &= 14 \\ 5R + 2C - 4A &= k \end{aligned}

If this system of linear equations is consistent (has at least one solution), what is the value of

k

?

Accepted Answer

32

Soru