Question

What’s the correct answer

Answer 1

Answer:

sundaes costs $
`5`.

banana splits costs $
`6`.

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]`

Method 1

Multiply the matrix equation to get,


`1(f)+0(b)=5`




`5(f)+4(b)=49`



`\Rightarrow f=5`

We do backward substitution to get,


`25+4b=49`


`4b=49-25`


`4b=24`


`b=6`



Method 2

The augmented matrix is


`\left[\begin{array}{ccc}1&0&|5\\5&4&|49\end{array}\right]`

We reduce to reduced row echelon form by performing the following row operations;


`R_2-5R_1\rightarrow R_2`.


`\left[\begin{array}{ccc}1&0&|5\\0&4&|24\end{array}\right]`

The next row operation is
`(1)/(4) R_2\rightarrow R_2`


`\left[\begin{array}{ccc}1&0&|5\\0&1&|6\end{array}\right]`

This implies that,


`f=5` and
`b=6`

The correct answer is B