You Invest in AAA-Rated Bonds, A-Rated Bonds, and B-Rated Bonds $x,$

Multiple Choice

You invest in AAA-rated bonds, A-rated bonds, and B-rated bonds. Your average yield is 8% on AAA bonds, 9% on A bonds, and 10% on B bonds. You invest twice as much in B bonds as in A bonds. The desired system of linear equations (where $x,$ $y,$ and $z$ represent the amounts invested in AAA, A, and B bonds, respectively) is as follows. $\left\{ \begin{aligned}x + y + z & = ( \text { total investment) } \\0.08 x + 0.09 y + 0.1 z & = \text { (annual return) } \\2 y - z & = 0\end{aligned} \right.$ Use the inverse of the coefficient matrix of this system to find the amount invested in B bonds for the given a total investment of $18,000 and annual return of $1640.

A) $8000
B) $6000
C) $9000
D) $1000
E) $2000