Answer:
sundaes costs $

.
banana splits costs $

.
Explanation:
The matrix equation that represents the system is
![\left[\begin{array}{cc}1&0\\5&4\\\end{array}\right] \left[\begin{array}{c}f\\b\\\end{array}\right] =\left[\begin{array}{c}5\\49\\\end{array}\right]](https://img.qammunity.org/2019/formulas/mathematics/middle-school/13hoqu5lsn5nm2kpfvtmdzj5o4xaofb5tw.png)
Method 1
Multiply the matrix equation to get,



We do backward substitution to get,




Method 2
The augmented matrix is
![\left[\begin{array}{ccc}1&0&|5\\5&4&|49\end{array}\right]](https://img.qammunity.org/2019/formulas/mathematics/middle-school/w7g668jb4zrwf5hak853vlme2fj92y3t6y.png)
We reduce to reduced row echelon form by performing the following row operations;

.
![\left[\begin{array}{ccc}1&0&|5\\0&4&|24\end{array}\right]](https://img.qammunity.org/2019/formulas/mathematics/middle-school/ctos73fmazuue8fae0yjfvo9498bq1u9d1.png)
The next row operation is

![\left[\begin{array}{ccc}1&0&|5\\0&1&|6\end{array}\right]](https://img.qammunity.org/2019/formulas/mathematics/middle-school/yecf4tdtkfi3maxkx9dc46q18pzjgdh8rq.png)
This implies that,

and

The correct answer is B