Question

What’s the correct answer

Answer 1

Answer:

sundaes costs $ $5$.

banana splits costs $ $6$.

Step-by-step 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 $\frac{1}{4} R_2\rightarrow R_2$

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

This implies that,

$f=5$ and $b=6$

The correct answer is B